def construct(self):
sub1 = CText('这将是一个')
sub2 = CText('关于线段长度的性质')
subs = VGroup(sub1, sub2)
subs.arrange(DOWN)
self.play(Write(sub1))
self.play(Write(sub2))
self.wait(2)
self.play(FadeOut(subs))
def construct(self):
text1 = CText('这是一条重要的性质')
text2 = CText('后面会经常用到')
group = VGroup(text1, text2)
group.arrange(DOWN)
self.play(Write(text1))
self.wait()
self.play(Write(text2))
self.wait()
self.play(FadeOut(group))
def construct(self):
sub1 = CText('根据性质1')
sub2 = CText('可以用另一种方法找到')
sub3 = CText('抛物线上的点')
subs = VGroup(sub1, sub2, sub3)
subs.arrange(DOWN)
self.play(Write(sub1))
self.wait()
self.play(Write(sub2))
self.wait()
self.play(Write(sub3))
self.wait(5)
self.play(FadeOut(subs))
def construct(self):
text = CText('总结')
text.set_fill(DARK_BROWN)
content1 = CText('抛物线任意弦与准线的交点')
content2 = CText('及该抛物线的焦点所构成的线段，')
content3 = CText('平分该弦两端点与焦点所构成角的外角')
contents = VGroup(content1, content2, content3)
contents.scale(0.7)
contents.arrange(DOWN)
total = VGroup(text, contents)
total.arrange(DOWN, buff=MED_LARGE_BUFF)
self.play(Write(text))
self.wait(2)
self.play(Write(contents))
self.wait(10)
def construct(self):
line1_1 = CText('抛物线')
line1_1.set_fill(DARK_BLUE)
line1_2 = CText('性质三')
line1 = VGroup(line1_1, line1_2)
line1.arrange(RIGHT)
line2 = CText('推论一')
lines = VGroup(line1, line2)
lines.arrange(DOWN, buff=LARGE_BUFF)
self.play(Write(line1))
self.wait(3)
self.play(Write(line2))
self.wait(3)
self.play(FadeOut(lines))
def construct(self):
text = CText('总结')
text.set_fill(DARK_BROWN)
content1 = CText('纵标线的平方等于')
content2 = CText('横标线与焦距乘积的四倍')
contents = VGroup(content1, content2)
contents.scale(0.7)
contents.arrange(DOWN)
total = VGroup(text, contents)
total.arrange(DOWN, buff=MED_LARGE_BUFF)
self.play(Write(text))
self.wait(2)
self.play(Write(contents))
self.wait(10)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 2
focusLabel = TexMobject('F').scale(0.5)
focusLabel.next_to(focus, RIGHT, buff=SMALL_BUFF)
self.play(*[ShowCreation(e) for\
e in [graph, directrix, focus, focusLabel]])
self.wait()
sub1 = CText('任取一点P').scale(0.3)
sub1.to_edge(RIGHT)
self.play(ShowCreation(sub1))
y_val = ValueTracker(6)
p = Dot()
p.plot_depth = 1
p.set_fill(DARK_BLUE)
p.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()),
y_val.get_value()
)))
self.play(ShowCreation(p))
p_label = TexMobject('P').scale(0.5)
p_label.plot_depth = 1
p_label.add_updater(lambda m:\
m.next_to(p, RIGHT, buff=SMALL_BUFF))
self.play(ShowCreation(p_label))
self.wait()
self.play(FadeOut(sub1))
sub2 = CText('过点P做抛物线的切线')
sub2.scale(0.3)
sub2.to_edge(RIGHT)
self.play(ShowCreation(sub2))
self.wait()
tangent = Line()
self.add_tangent_line_updater(tangent, p)
# self.play(ShowCreation(tangent))
# self.wait()
tangent_extent = Line()
def get_extent(l, p, t):
l.put_start_and_end_on(LEFT * 10, RIGHT * 10)
l.set_angle(t.get_angle() + PI)
l.move_to(p.get_center())
tangent_extent.add_updater(lambda l:\
get_extent(l, p, tangent))
tangent_line = VGroup()
tangent_line.add(tangent)
tangent_line.add(tangent_extent)
self.play(ShowCreation(tangent_extent))
self.add(tangent_line)
self.wait()
self.play(FadeOut(sub2))
sub3 = CText('交准线于Z').scale(0.3)
sub3.to_edge(RIGHT)
self.play(ShowCreation(sub3))
self.wait()
z = Dot()
z.plot_depth = 1
z.set_fill(DARK_BLUE)
z.add_updater(lambda m:\
m.move_to(self.get_tangent_to_directrix(p)))
self.play(ShowCreation(z))
z_label = TexMobject('Z').scale(0.5)
z_label.plot_depth = 1
z_label.add_updater(lambda m:\
m.next_to(z, LEFT, buff=SMALL_BUFF))
self.play(ShowCreation(z_label))
self.wait()
self.play(FadeOut(sub3))
sub4 = CText('交正焦弦于点K').scale(0.3)
sub4.to_edge(RIGHT)
self.play(ShowCreation(sub4))
self.wait()
def find_k():
start = z.get_center()
vec = p.get_center() - start
vec /= vec[0]
d = focus.get_center()[0] - start[0]
vec *= d
return start + vec
k = Dot()
k.plot_depth = 1
k.set_fill(DARK_BLUE)
k.add_updater(lambda m:\
m.move_to(find_k()))
k_label = TexMobject('K').scale(0.5)
k_label.plot_depth = 1
k_label.add_updater(lambda m:\
m.next_to(k, RIGHT, buff=SMALL_BUFF))
def find_opp():
pos = find_k()
fac = -1
if pos[1] < 0:
fac = 1
return self.coords_to_point(self.func(self.focus * 2),
fac * self.focus * 2)
k_line = Line()
k_line.add_updater(lambda m:\
m.put_start_and_end_on(
find_k(),
find_opp()
))
self.play(ShowCreation(k_line))
self.play(ShowCreation(k))
self.play(ShowCreation(k_label))
self.wait()
self.play(FadeOut(sub4))
sub5 = CText('则ZF=KF').scale(0.3)
sub5.to_edge(RIGHT)
self.play(ShowCreation(sub5))
self.wait()
zf = Line()
zf.set_color(RED)
zf.add_updater(lambda m:\
m.put_start_and_end_on(
z.get_center(),
focus.get_center()
))
kf = Line()
kf.set_color(RED)
kf.add_updater(lambda m:\
m.put_start_and_end_on(
k.get_center(),
focus.get_center()
))
self.play(ShowCreation(zf), ShowCreation(kf))
self.wait()
self.play(y_val.set_value, 9, rate_func=easeOutElastic, run_time=2)
self.wait()
self.play(y_val.set_value, 1, rate_func=easeOutBounce, run_time=2)
self.wait()
self.play(y_val.set_value, -6, rate_func=easeOutElastic, run_time=2)
self.wait()
self.play(y_val.set_value, 8, rate_func=easeOutBounce, run_time=2)
self.wait()
self.play(FadeOut(sub5))
m = Dot()
m.plot_depth = 1
m.set_fill(YELLOW)
m.add_updater(lambda e:\
e.move_to(z.get_center()[0] * RIGHT +
p.get_center()[1] * UP))
m_label = TexMobject('M').scale(0.5)
m_label.add_updater(lambda e:\
e.next_to(m, LEFT, buff=SMALL_BUFF))
self.play(ShowCreation(m))
self.play(ShowCreation(m_label))
mp = DashedLine()
mp.add_updater(lambda l:\
l.put_start_and_end_on(
m.get_center(),
p.get_center()
))
self.play(ShowCreation(mp))
fp = DashedLine()
fp.add_updater(lambda l:\
l.put_start_and_end_on(
focus.get_center(),
p.get_center()
))
self.play(ShowCreation(fp))
self.wait()
km = DashedLine()
km.add_updater(lambda l:\
l.put_start_and_end_on(
k.get_center(),
m.get_center()
))
self.play(ShowCreation(km))
k2 = Dot()
k2.plot_depth = 1
k2.set_fill(YELLOW)
k2.add_updater(lambda m:\
m.move_to(
k.get_center()[1] * UP +
z.get_center()[0] * RIGHT
))
self.play(ShowCreation(k2))
k2_label = TexMobject('K\'').scale(0.5)
k2_label.add_updater(lambda m:\
m.next_to(k2, LEFT, buff=SMALL_BUFF))
self.play(ShowCreation(k2_label))
kk2 = DashedLine()
kk2.add_updater(lambda l:\
l.put_start_and_end_on(
k.get_center(),
k2.get_center()
))
self.play(ShowCreation(kk2))
z2 = Dot()
z2.plot_depth = 1
z2.set_fill(YELLOW)
z2.add_updater(lambda m:\
m.move_to(
z.get_center()[1] * UP +
focus.get_center()[0] * RIGHT
))
self.play(ShowCreation(z2))
z2f = Line()
z2f.plot_depth = -1
z2f.add_updater(lambda l:\
l.put_start_and_end_on(
z2.get_center(),
focus.get_center()
))
self.add(z2f)
z2_label = TexMobject('Z\'').scale(0.5)
z2_label.add_updater(lambda m:\
m.next_to(z2, UR, buff=SMALL_BUFF))
self.play(ShowCreation(z2_label))
zz2 = DashedLine()
zz2.add_updater(lambda l:\
l.put_start_and_end_on(
z.get_center(),
z2.get_center()
))
self.play(ShowCreation(zz2))
self.wait()
self.play(kk2.set_color, RED)
self.play(zz2.set_color, RED)
proof = VGroup()
proof1 = CText('证明思路').scale(0.3)
proof2 = TexMobject('KK\'=ZZ\'').scale(0.5)
proof3 = TexMobject('\\triangle ZKM \\cong \\triangle ZKF')
proof3.scale(0.5)
proof.add(proof1)
proof.add(proof2)
proof.add(proof3)
proof.arrange(DOWN)
proof.to_edge(RIGHT, buff=LARGE_BUFF)
proof2.align_to(proof1, LEFT)
proof3.align_to(proof2, LEFT)
self.play(ShowCreation(proof))
self.wait(5)
zkm = Polygon(z.get_center(), k.get_center(), m.get_center())
zkm.set_fill(DARK_BLUE, opacity=0.5)
zkf = Polygon(z.get_center(), k.get_center(), focus.get_center())
zkf.set_fill(DARK_BLUE, opacity=0.5)
self.play(ShowCreationThenDestruction(zkm),
ShowCreationThenDestruction(zkf))
self.wait(15)
self.play(y_val.set_value, 1, rate_func=easeOutBounce)
self.wait(5)
self.play(y_val.set_value, -1, rate_func=easeOutElastic)
self.wait(5)
self.play(y_val.set_value, -8, rate_func=easeOutBounce)
self.wait(5)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focusLabel = TexMobject('F').scale(0.5)
focusLabel.next_to(focus, RIGHT, buff=SMALL_BUFF)
self.play(*[ShowCreation(e) for\
e in [graph, directrix, focus, focusLabel]])
sub1 = CText('P1P2为抛物线正焦弦').scale(0.3)
sub1.to_edge(RIGHT)
self.wait(2)
self.play(Write(sub1))
p1 = Dot()
p1.move_to(self.coords_to_point(self.focus, 2 * self.focus))
p1.plot_depth = 1
p1.set_fill(DARK_BROWN)
p2 = Dot()
p2.move_to(self.coords_to_point(self.focus, -2 * self.focus))
p2.plot_depth = 1
p2.set_fill(DARK_BROWN)
p1_label = TexMobject('P_1').scale(0.5)
p1_label.next_to(p1, RIGHT)
p2_label = TexMobject('P_2').scale(0.5)
p2_label.next_to(p2, RIGHT)
self.play(ShowCreation(p1), ShowCreation(p2))
self.play(ShowCreation(Line(p1, p2)))
self.play(ShowCreation(p1_label), ShowCreation(p2_label))
self.wait()
x = Dot()
x.move_to(self.coords_to_point(-self.focus, 0))
x.set_fill(DARK_BROWN)
x.plot_depth = 1
x_label = TexMobject('X').scale(0.5)
x_label.next_to(x, LEFT)
sub2 = CText('X为轴与准线的交点').scale(0.3)
sub2.to_edge(RIGHT)
self.play(FadeOut(sub1))
self.play(FadeIn((sub2)))
self.wait()
h_line = Line(focus, x)
h_line.plot_depth = 2
self.play(ShowCreation(h_line))
self.play(ShowCreation(x))
self.play(FadeOut(h_line))
self.play(Write(x_label))
self.wait()
sub3 = CText('则P1与P2的切线交于X').scale(0.3)
sub3.to_edge(RIGHT)
self.play(FadeOut(sub2))
self.play(Write(sub3))
p1_tangent = Line()
self.add_tangent_line_updater(p1_tangent, p1)
p2_tangent = Line()
self.add_tangent_line_updater(p2_tangent, p2)
self.play(ShowCreation(p1_tangent), ShowCreation(p2_tangent))
self.wait()
self.play(ShowCreation(DashedLine(x, focus)))
m1 = Dot()
m1.move_to(self.coords_to_point(-self.focus, 2 * self.focus))
m1.set_fill(DARK_BROWN)
m1.plot_depth = 1
m1_label = TexMobject('M_1').scale(0.5)
m1_label.next_to(m1, LEFT)
self.play(ShowCreation(m1))
self.play(ShowCreation(m1_label))
self.play(ShowCreation(DashedLine(p1, m1)))
sub4 = CText('在正方形XFP1M1中，XP1是对角线')
sub4.scale(0.3)
sub4.to_edge(RIGHT)
self.play(FadeOut(sub3))
self.play(Write(sub4))
self.wait(5)
self.play(
ShowCreationThenDestruction(
Polygon(x.get_center(), focus.get_center(), p1.get_center(),
m1.get_center())))
sub5 = CText('XP1也正好平分角M1P1F，因此是过P1点的切线')
sub5.scale(0.3)
sub5.to_edge(RIGHT)
self.wait(5)
self.play(FadeOut(sub4))
self.play(Write(sub5))
sub6 = CText('同理，P2X也为切线')
sub6.scale(0.3)
sub6.to_edge(RIGHT)
self.wait(5)
self.play(FadeOut(sub5))
self.play(Write(sub6))
sub7 = CText('总结：抛物线正焦弦端点切线交于准线与轴的交点')
sub7.scale(0.3)
sub7.to_edge(RIGHT)
self.wait(5)
self.play(FadeOut(sub6))
self.play(Write(sub7))
self.wait(10)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focusLabel = TexMobject('F').scale(0.5)
focusLabel.next_to(focus, RIGHT, buff=SMALL_BUFF)
self.play(*[ShowCreation(e) for\
e in [graph, directrix, focus, focusLabel]])
y_val = ValueTracker(8)
p = Dot()
p.plot_depth = 1
p.set_fill(DARK_BLUE)
p.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()),
y_val.get_value()
)))
p_label = TexMobject('P').scale(0.5)
p_label.plot_depth = 1
p_label.add_updater(lambda m:\
m.next_to(p, RIGHT, buff=SMALL_BUFF))
k = Dot()
k.plot_depth = 1
k.set_fill(DARK_BLUE)
k.add_updater(lambda m:\
m.move_to(self.get_tangent_to_directrix(
p
)))
k_label = TexMobject('K').scale(0.5)
k_label.plot_depth = 1
k_label.add_updater(lambda m:\
m.next_to(k, LEFT, buff=SMALL_BUFF))
tangent = Line()
self.add_tangent_line_updater(tangent, p)
self.play(ShowCreation(p))
self.play(ShowCreation(p_label))
self.play(ShowCreation(tangent))
self.play(ShowCreation(k))
self.play(ShowCreation(k_label))
def get_extent(l):
l.put_start_and_end_on(p.get_center(), RIGHT * 10)
l.set_angle(tangent.get_angle() + PI)
tangent_extent = Line()
tangent_extent.add_updater(lambda l:\
get_extent(l))
self.play(ShowCreation(tangent_extent))
self.wait()
m = Dot()
m.set_fill(DARK_BLUE)
m.plot_depth = 1
m.add_updater(lambda e:\
e.move_to(self.coords_to_point(
-self.focus,
y_val.get_value()
)))
m_label = TexMobject('M').scale(0.5)
m_label.add_updater(lambda e:\
e.next_to(m, LEFT, buff=SMALL_BUFF))
mp = Line()
mp.add_updater(lambda l:\
l.put_start_and_end_on(
p.get_center(),
self.coords_to_point(
-self.focus,
y_val.get_value()
)))
fp = Line()
fp.add_updater(lambda l:\
l.put_start_and_end_on(
focus.get_center(),
p.get_center()
))
self.play(ShowCreation(mp), ShowCreation(fp))
self.play(ShowCreation(m))
self.play(ShowCreation(m_label))
kf = Line()
kf.add_updater(lambda l:\
l.put_start_and_end_on(
k.get_center(),
focus.get_center()
))
self.play(ShowCreation(kf))
self.wait()
sub1 = CText('在切线上任取一点O')
sub1.scale(0.3)
sub1.to_edge(RIGHT)
self.play(Write(sub1))
self.wait()
ot = ValueTracker(0.2)
vec_kp = p.get_center() - k.get_center()
o = Dot()
o.plot_depth = 1
o.set_fill(RED)
o.add_updater(lambda m:\
m.move_to(k.get_center() +\
vec_kp * ot.get_value()))
o_label = TexMobject('O').scale(0.5)
o_label.plot_depth = 1
o_label.add_updater(lambda m:\
m.next_to(o, DR, buff=SMALL_BUFF))
self.play(ShowCreation(o))
self.play(ShowCreation(o_label))
self.wait()
sub2 = CText('则OM=OF')
sub2.scale(0.3)
sub2.to_edge(RIGHT)
self.play(FadeOut(sub1))
self.play(Write(sub2))
self.wait()
om = Line()
om.add_updater(lambda l:\
l.put_start_and_end_on(
o.get_center(),
m.get_center()
))
of = Line()
of.add_updater(lambda l:\
l.put_start_and_end_on(
o.get_center(),
focus.get_center()
))
self.play(ShowCreation(om), ShowCreation(of))
self.wait()
self.play(ot.set_value, 0.05)
self.wait()
self.play(ot.set_value, 0.8)
self.wait()
self.play(ot.set_value, 1.2)
self.wait()
self.play(ot.set_value, 0.6)
self.wait(3)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focusLabel = TexMobject('F').scale(0.5)
focusLabel.next_to(focus, DOWN, buff=SMALL_BUFF)
focusLabel.plot_depth = 1
self.play(*[ShowCreation(e) for\
e in [graph, focus, focusLabel]])
h_line = Line(self.coords_to_point(0, 0), ORIGIN)
h_line.plot_depth = -1
self.play(ShowCreation(h_line))
a = Dot()
a.move_to(self.coords_to_point(0, 0))
a.plot_depth = 1
a.set_fill(DARK_BROWN)
a_label = TexMobject('A').scale(0.5)
a_label.next_to(a, DL, buff=SMALL_BUFF)
a_label.plot_depth = 1
self.play(
ShowCreation(a),
Write(a_label)
)
self.wait()
y_val = ValueTracker(6.5)
p1 = Dot()
p1.set_fill(DARK_BLUE)
p1.plot_depth = 1
p1.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()),
y_val.get_value()
)))
p1_label = TexMobject('P_1').scale(0.5)
p1_label.plot_depth = 1
p1_label.add_updater(lambda m:\
m.next_to(p1, RIGHT, buff=SMALL_BUFF))
p2 = Dot()
p2.set_fill(DARK_BLUE)
p2.plot_depth = 1
p2.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(-y_val.get_value()),
-y_val.get_value()
)))
p2_label = TexMobject('P_2').scale(0.5)
p2_label.plot_depth = 1
p2_label.add_updater(lambda m:\
m.next_to(p2, RIGHT, buff=SMALL_BUFF))
p1p2 = Line()
p1p2.add_updater(lambda m:\
m.put_start_and_end_on(
self.coords_to_point(
self.func(y_val.get_value()),
y_val.get_value()
),
self.coords_to_point(
self.func(-y_val.get_value()),
-y_val.get_value()
)))
self.play(
ShowCreation(p1),
Write(p1_label)
)
self.play(ShowCreation(p1p2))
self.play(
ShowCreation(p2),
Write(p2_label)
)
self.wait()
n1 = Dot()
n1.set_fill(DARK_BLUE)
n1.plot_depth = 1
n1.add_updater(lambda m:\
m.move_to(p1.get_center()[0] * RIGHT))
n1_label = TexMobject('N').scale(0.5)
n1_label.add_updater(lambda m:\
m.next_to(n1, DR, buff=SMALL_BUFF))
self.play(
ShowCreation(n1),
Write(n1_label)
)
self.wait()
q_y = ValueTracker(5)
q = Dot()
q.set_fill(DARK_BLUE)
q.plot_depth = 1
q.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(q_y.get_value()),
q_y.get_value()
)))
q_label = TexMobject('Q').scale(0.5)
q_label.plot_depth = 1
q_label.add_updater(lambda m:\
m.next_to(q, LEFT, buff=SMALL_BUFF))
self.play(
ShowCreation(q),
Write(q_label)
)
self.wait()
def get_l():
qy = q_y.get_value()
qx = self.func(qy)
py = y_val.get_value()
px = self.func(py)
l = qy / qx * px
return self.coords_to_point(px, l)
l = Dot()
l.set_fill(DARK_BLUE)
l.plot_depth = 1
l.add_updater(lambda m:\
m.move_to(get_l()))
l_label = TexMobject('L').scale(0.5)
l_label.add_updater(lambda m:\
m.next_to(l, RIGHT, buff=SMALL_BUFF))
al = Line()
al.add_updater(lambda m:\
m.put_start_and_end_on(
a.get_center(),
get_l() if\
q_y.get_value() < y_val.get_value()\
else q.get_center()
))
p1l = Line()
p1l.add_updater(lambda m:\
m.put_start_and_end_on(
p1.get_center(),
get_l()
))
self.play(
ShowCreation(al),
ShowCreation(p1l))
self.play(
ShowCreation(l),
Write(l_label)
)
self.wait()
def get_l2():
qy = q.get_center()[1]
px = p1.get_center()[0]
return px * RIGHT + qy * UP
l2 = Dot()
l2.set_fill(DARK_BLUE)
l2.plot_depth = 1
l2.add_updater(lambda m:\
m.move_to(get_l2()))
l2_label = TexMobject("L'").scale(0.5)
l2_label.add_updater(lambda m:\
m.next_to(l2, RIGHT, buff=SMALL_BUFF))
ql2 = Line()
ql2.add_updater(lambda m:\
m.put_start_and_end_on(
q.get_center(),
get_l2()
))
p1l2 = Line()
p1l2.add_updater(lambda m:\
m.put_start_and_end_on(
p1.get_center(),
get_l2()
))
self.play(
ShowCreation(ql2),
ShowCreation(p1l2))
self.play(
ShowCreation(l2),
Write(l2_label)
)
corollary = VGroup()
head = CText('推论：').scale(0.25)
head.set_fill(DARK_BLUE)
crlly = TexMobject("P_1N^2=LN\\cdot L'N").scale(0.5)
head_line = VGroup(head, crlly)
head_line.arrange(RIGHT)
proof = VGroup()
proof_head = CText('证明：').scale(0.25)
proof_head.set_fill(DARK_BLUE)
proof.add(proof_head)
proof_details = VGroup()
prf1 = TexMobject("\\frac{LN}{AN}=\\frac{QN'}{AN'}")\
.scale(0.5)
prf2 = VGroup()
prf2_1 = CText('又').scale(0.25)
prf2_2 = TexMobject(
"\\because L'N=QN'")\
.scale(0.5)
prf2.add(prf2_1, prf2_2)
prf2.arrange(RIGHT, buff=SMALL_BUFF)
prf3 = TexMobject(
"\\therefore LN\\cdot L'N=\\frac{QN'\
\\cdot AN}{AN'}\\cdot QN' =\
\\frac{QN'^2\\cdot AN}{AN'}"
).scale(0.5)
prf4 = VGroup()
prf4_1 = CText('又').scale(0.25)
prf4_2 = TexMobject(
"\\because QN'^2=4AN'\\cdot AF")\
.scale(0.5)
prf4.add(prf4_1, prf4_2)
prf4.arrange(RIGHT, buff=SMALL_BUFF)
prf5 = TexMobject(
"\\therefore LN\\cdot L'N=\\frac{4AN'\\cdot AF\
\\cdot AN}{AN'} = 4AN\\cdot AF = P_1N^2"
).scale(0.5)
proof_details.add(prf1, prf2, prf3,
prf4, prf5)
proof_details.arrange(DOWN)
proof.add(proof_details)
proof.arrange(RIGHT)
proof_details.align_to(proof_head, UP)
corollary.add(head_line)
corollary.add(proof)
corollary.arrange(DOWN)
head_line.align_to(proof, LEFT)
prf1.align_to(crlly, LEFT)
for e in [prf2, prf3, prf4, prf5]:
e.align_to(prf1, LEFT)
corollary.to_edge(RIGHT)
self.play(Write(head_line))
self.wait()
def get_n2():
qx = q.get_center()[0]
return qx * RIGHT
n2 = Dot()
n2.plot_depth = 1
n2.set_fill(DARK_BLUE)
n2.add_updater(lambda m:\
m.move_to(get_n2()))
n2_label = TexMobject("N'").scale(0.5)
n2_label.add_updater(lambda m:\
m.next_to(n2, DOWN, buff=SMALL_BUFF))
qn2 = DashedLine()
qn2.add_updater(lambda m:\
m.put_start_and_end_on(
q.get_center(),
get_n2()
))
self.play(ShowCreation(qn2))
self.play(
ShowCreation(n2),
Write(n2_label)
)
self.wait()
self.play(
Write(proof_head),
Write(prf1))
self.wait(3)
self.play(ShowCreationThenDestruction(
Polygon(
a.get_center(),
n2.get_center(),
q.get_center())
))
self.wait()
self.play(ShowCreationThenDestruction(
Polygon(
a.get_center(),
n1.get_center(),
l.get_center())
))
for e in [prf2, prf3, prf4, prf5]:
self.wait(3)
self.play(Write(e))
self.wait(10)
self.play(y_val.set_value, 4)
self.play(q_y.set_value, 8)
self.wait(10)
def construct(self):
text1head = CText('高中时期的解析几何都用')
text1body = CText('坐标系')
text1tail = CText('进行研究')
text1 = VGroup(text1head, text1body, text1tail, buff=SMALL_BUFF)
text1.arrange()
text1body.set_fill(DARK_BLUE)
text2 = CText('计算繁杂，且不优雅')
text3head = CText('那么，是否可以用')
text3body = CText('纯几何')
text3tail = CText('的方法')
text3 = VGroup(text3head, text3body, text3tail, buff=SMALL_BUFF)
text3body.set_fill(DARK_BLUE)
text3.arrange()
# text2[1].set_fill(DARK_BLUE)
text4 = CText('来得到一些圆锥曲线的性质？')
group = VGroup(text1, text2, text3, text4)
group.arrange_submobjects(direction=DOWN, buff=1)
group.scale(0.5)
self.play(Write(text1))
self.play(WiggleOutThenIn(text1body))
self.wait()
self.play(Write(text2))
self.wait()
self.play(Write(text3))
self.play(WiggleOutThenIn(text3body))
self.wait()
self.play(Write(text4))
self.wait(2)
self.play(FadeOut(group))
explan1 = CText('本系列将试图用几何方法研究圆锥曲线')
explan2h = CText('主要参考')
explan2t = CText('《圆锥曲线的几何性质》')
explan2 = VGroup(explan2h, explan2t)
explan2.arrange()
explan2t.set_fill(DARK_BLUE)
explan3 = CText('希望能有所帮助')
explan = VGroup(explan1, explan2, explan3)
explan.arrange_submobjects(direction=DOWN, buff=1)
explan.scale(0.5)
self.play(Write(explan1))
self.wait()
self.play(Write(explan2))
self.play(WiggleOutThenIn(explan2t))
self.wait()
self.play(Write(explan3))
self.wait(2)
self.play(FadeOut(explan))
jokeh = CText('视频使用')
jokeb = CText('manim')
joket = CText('制作')
jokeb.set_fill(DARK_BLUE)
joked = CText('边学边做，随缘更新')
jokeT = VGroup(jokeh, jokeb, joket, buff=SMALL_BUFF)
jokeT.arrange()
joke = VGroup(jokeT, joked)
joke.arrange_submobjects(direction=DOWN, buff=1)
self.play(Write(jokeT))
self.play(WiggleOutThenIn(jokeb))
self.wait()
self.play(Write(joked))
self.wait(2)
self.play(FadeOut(joke))
last = CText('从抛物线开始')
self.play(Write(last))
self.wait()
self.play(FadeOut(last))
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focusLabel = TexMobject('F').scale(0.7)
focusLabel.next_to(focus, RIGHT)
self.play(*[ShowCreation(e) for\
e in [graph, directrix, focus, focusLabel]])
q1_y = ValueTracker(9)
q1 = Dot()
q1.set_fill(DARK_BLUE)
q1.plot_depth = 1
q1.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(q1_y.get_value()),
q1_y.get_value()
)))
q1_label = TexMobject('Q_1').scale(0.5)
q1_label.add_updater(lambda m:\
m.next_to(q1, RIGHT, buff=SMALL_BUFF))
self.play(ShowCreation(q1), ShowCreation(q1_label))
q2 = Dot()
q2.set_fill(DARK_BLUE)
q2.plot_depth = 1
q2.add_updater(lambda m:\
m.move_to(self.get_opposite(q1)))
q2_label = TexMobject('Q_2').scale(0.5)
q2_label.add_updater(lambda m:\
m.next_to(q2, RIGHT, buff=SMALL_BUFF))
q1q2 = Line()
q1q2.add_updater(lambda m:\
m.put_start_and_end_on(
q1.get_center(),
self.get_opposite(q1)
))
self.play(*[ShowCreation(e) for e in\
[q2, q2_label, q1q2]])
p1_y = ValueTracker(2)
p1 = Dot()
p1.set_fill(DARK_BLUE)
p1.plot_depth = 1
p1.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(p1_y.get_value()),
p1_y.get_value()
)))
p1_label = TexMobject('P_1').scale(0.5)
p1_label.add_updater(lambda m:\
m.next_to(p1, RIGHT, buff=SMALL_BUFF))
self.play(ShowCreation(p1), ShowCreation(p1_label))
p2 = Dot()
p2.set_fill(DARK_BLUE)
p2.plot_depth = 1
p2.add_updater(lambda m:\
m.move_to(self.get_opposite(p1)))
p2_label = TexMobject('P_2').scale(0.5)
p2_label.add_updater(lambda m:\
m.next_to(p2, RIGHT, buff=SMALL_BUFF))
p1p2 = Line()
p1p2.add_updater(lambda m:\
m.put_start_and_end_on(
p1.get_center(),
self.get_opposite(p1)
))
self.play(*[ShowCreation(e) for e in\
[p2, p2_label, p1p2]])
k1 = Dot()
k1.set_fill(DARK_BROWN)
k1.plot_depth = 1
k1.add_updater(lambda m:\
m.move_to(self.chord_to_directrix(p1, q1)))
k1_label = TexMobject('K_1').scale(0.5)
k1_label.add_updater(lambda m:\
m.next_to(k1, LEFT, buff=SMALL_BUFF))
p1q1 = Line()
p1q1.add_updater(lambda m:\
m.put_start_and_end_on(
self.right(p1, q1),
self.chord_to_directrix(p1, q1)
))
p2q2 = Line()
p2q2.add_updater(lambda m:\
m.put_start_and_end_on(
self.right(p2, q2),
self.chord_to_directrix(p2, q2)
))
self.play(*[ShowCreation(e) for e in \
[k1, k1_label, p1q1, p2q2]])
k2 = Dot()
k2.set_fill(DARK_BROWN)
k2.plot_depth = 1
k2.add_updater(lambda m:\
m.move_to(self.chord_to_directrix(p2, q1)))
k2_label = TexMobject('K_2').scale(0.5)
k2_label.add_updater(lambda m:\
m.next_to(k2, LEFT, buff=SMALL_BUFF))
p2q1 = Line()
p2q1.add_updater(lambda m:\
m.put_start_and_end_on(
self.right(p2, q1),
self.chord_to_directrix(p2, q1)
))
p1q2 = Line()
p1q2.add_updater(lambda m:\
m.put_start_and_end_on(
self.right(p1, q2),
self.chord_to_directrix(p1, q2)
))
self.play(*[ShowCreation(e) for e in \
[k2, k2_label, p2q1, p1q2]])
explain = CText('这些交点在准线上').scale(0.3)
explain.to_edge(RIGHT)
self.wait(2)
self.play(Write(explain))
self.wait(5)
self.play(ApplyMethod(q1_y.set_value, 0.5),
ApplyMethod(p1_y.set_value, -3))
self.wait(3)
self.play(ApplyMethod(q1_y.set_value, 3),
ApplyMethod(p1_y.set_value, -9))
self.wait(10)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=DARK_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
self.play(ShowCreation(graph), ShowCreation(directrix),
ShowCreation(focus))
focus_label = TexMobject('F').scale(0.5)
focus_label.next_to(focus, DOWN, buff=SMALL_BUFF)
self.play(Write(focus_label))
h_line = Line()
d_loc = directrix.get_center()[0] * RIGHT
h_line.put_start_and_end_on(d_loc, ORIGIN)
h_line.plot_depth = -1
self.play(ShowCreation(h_line))
a = Dot()
a.set_fill(LIGHT_BROWN)
a.plot_depth = 1
a.move_to(self.coords_to_point(0, 0))
a_label = TexMobject('A').scale(0.5)
a_label.next_to(a, DL, buff=SMALL_BUFF)
t = Dot()
t.set_fill(LIGHT_BROWN)
t.plot_depth = 1
t.move_to(d_loc)
t_label = TexMobject('T').scale(0.5)
t_label.next_to(t, LEFT, buff=SMALL_BUFF)
y_value = ValueTracker(9)
p = Dot()
p.set_fill(DARK_BLUE)
p.plot_depth = 1
p.add_updater(lambda m:\
m.move_to(self.value_to_point(
y_value.get_value())))
p_label = TexMobject('P').scale(0.5)
p_label.add_updater(lambda m:\
m.next_to(p, RIGHT, buff=SMALL_BUFF))
m = Dot()
m.set_fill(DARK_BLUE)
m.plot_depth = 1
m.add_updater(lambda t:\
t.move_to(d_loc + p.get_center()[1] * UP))
m_label = TexMobject('M').scale(0.5)
m_label.add_updater(lambda l:\
l.next_to(m, LEFT, buff=SMALL_BUFF))
n = Dot()
n.set_fill(DARK_BLUE)
n.plot_depth = 1
n.add_updater(lambda m:\
m.move_to(p.get_center()[0] * RIGHT))
n_label = TexMobject('N').scale(0.5)
n_label.add_updater(lambda m:\
m.next_to(n, DOWN, buff=SMALL_BUFF))
self.play(*[ShowCreation(e) for e in\
[a, p, m, n, t]])
self.play(*[ShowCreation(e) for e in\
[a_label, t_label, p_label, m_label, n_label]])
self.wait()
pn = Line()
pn.add_updater(lambda l:\
l.put_start_and_end_on(
p.get_center(), n.get_center()))
pf = Line()
pf.add_updater(lambda l:\
l.put_start_and_end_on(
p.get_center(), focus.get_center()))
pm = Line()
pm.add_updater(lambda l:\
l.put_start_and_end_on(
p.get_center(), m.get_center()))
self.play(*[ShowCreation(e) for e in\
[pn, pf, pm]])
self.wait()
prop = VGroup()
prop.add(CText('性质：')\
.scale(0.25).set_color(DARK_BLUE))
prop.add(TexMobject('PN^2=4AF\\cdot AN')\
.scale(0.5)).set_color(DARK_BROWN)
prop.arrange(RIGHT)
proof = VGroup()
prf = CText('证明：')\
.scale(0.25).set_color(DARK_BLUE)
proof.add(prf)
details = VGroup()
line1 = TexMobject('TN^2=', '(TA+AN)^2')\
.scale(0.5)
details.add(line1)
line2 = TexMobject('TN^2=PM^2=PF^2')\
.scale(0.5)
details.add(line2)
line3 = TexMobject('PF^2=PN^2+NF^2')\
.scale(0.5)
details.add(line3)
line4 = TexMobject(
'PN^2+NF^2=NF^2+4 AF\\cdot AN')\
.scale(0.5)
details.add(line4)
line5 = TexMobject('PN^2=4AF\\cdot AN').scale(0.5).set_color(
DARK_BROWN)
details.add(line5)
proof.add(details)
details.arrange(DOWN)
line2.align_to(line1, LEFT)
line3.align_to(line2, LEFT)
line4.align_to(line3, LEFT)
line5.align_to(line4, LEFT)
proof.arrange(RIGHT)
prf.align_to(details, UP)
forms = VGroup()
forms.add(prop)
forms.add(proof)
forms.arrange(DOWN)
proof.align_to(prop, LEFT)
forms.to_edge(RIGHT, buff=2)
expand = TexMobject('TA',
'^2+AN^2+2', 'TA',
'\\cdot AN')\
.scale(0.5)
expand.align_to(line1[1], LEFT)
expand.align_to(line1[1], UP)
expand2 = TexMobject('AF',
'^2+AN^2+2', 'AF',
'\\cdot AN')\
.scale(0.5)
expand2.align_to(line1[1], LEFT)
expand2.align_to(line1[1], UP)
expand3 = TexMobject(
'(AF-AN)^2+4 AF\\cdot AN')\
.scale(0.5)
expand3.align_to(line1[1], LEFT)
expand3.align_to(line1[1], UP)
expand4 = TexMobject('NF^2+4 AF\\cdot AN').scale(0.5)
expand4.align_to(line1[1], LEFT)
expand4.align_to(line1[1], UP)
self.play(Write(prop))
self.wait()
self.play(y_value.set_value, 1)
self.wait()
self.play(y_value.set_value, 3)
self.wait()
self.play(Write(prf))
self.play(Write(line1))
self.wait()
self.play(ShowCreationThenDestruction(Line(t, n).set_color(RED)))
self.play(ShowCreationThenDestruction(Line(t, a).set_color(RED)))
self.play(ShowCreationThenDestruction(Line(a, n).set_color(RED)))
self.wait()
self.play(ReplacementTransform(line1[1], expand))
self.wait(3)
self.play(ShowCreationThenDestruction(Line(t, a).set_color(RED)))
self.play(ShowCreationThenDestruction(Line(a, focus).set_color(RED)))
self.wait()
self.play(*[Transform(
expand[e], expand2[e]) for e in\
[0, 2]])
self.wait(3)
self.play(ReplacementTransform(expand, expand3))
self.wait(3)
self.play(ReplacementTransform(expand3, expand4))
self.wait(3)
self.play(Write(line2))
self.play(ShowCreationThenDestruction(Line(t, n).set_color(RED)))
self.play(ShowCreationThenDestruction(Line(p, m).set_color(RED)))
self.play(ShowCreationThenDestruction(Line(p, focus).set_color(RED)))
self.wait(3)
self.play(Write(line3))
self.play(
ShowCreationThenDestruction(
Polygon(p.get_center(), n.get_center(),
focus.get_center()).set_fill(DARK_BLUE, opacity=1)))
self.wait(3)
self.play(WiggleOutThenIn(expand4), WiggleOutThenIn(line3))
self.play(Write(line4))
self.wait(3)
self.play(Write(line5))
self.wait(3)
def1 = CText('AF是焦距')
def2 = CText('AN是点P的横标线')
def3 = CText('PN是点P的纵标线')
defines = VGroup(def1, def2, def3)
defines.arrange(DOWN)
defines.scale(0.25)
defines.next_to(proof, DOWN)
self.play(Write(defines))
self.wait(5)
self.play(y_value.set_value, 8)
self.wait(10)
def construct(self):
self.adjust_x_range()
sub1 = CText('已知准线与焦点')
sub1.scale(0.3)
sub1.to_edge(RIGHT)
self.play(Write(sub1))
directrix = self.get_directrix()
focus = Dot()
focus.move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focus_label = TexMobject('F').scale(0.5)
focus_label.next_to(focus, RIGHT + UP,\
buff=SMALL_BUFF)
self.play(*[ShowCreation(e) for e in [directrix, focus, focus_label]])
sub2 = CText('先找到顶点A')
sub2.scale(0.3)
sub2.to_edge(RIGHT)
self.wait()
self.play(FadeOut(sub1))
self.play(Write(sub2))
fl = Line(directrix.get_center(), focus.get_center())
a = Dot()
a.move_to(fl.get_center())
a.set_fill(DARK_BROWN)
a.plot_depth = 1
a_label = TexMobject('A').scale(0.5)
a_label.next_to(a, RIGHT + UP,\
buff=SMALL_BUFF)
self.play(ShowCreation(fl))
self.play(ShowCreation(a))
self.play(FadeOut(fl), ShowCreation(a_label))
y_val = ValueTracker(4)
sub3 = CText('在准线上任取一点')
sub3.scale(0.3)
sub3.to_edge(RIGHT)
self.play(FadeOut(sub2))
self.play(Write(sub3))
m = Dot()
m.set_fill(DARK_BLUE)
m.plot_depth = 1
m.add_updater(lambda m:\
m.move_to(self.coords_to_point(
-self.focus, y_val.get_value()
)))
m_label = TexMobject('M').scale(0.5)
m_label.add_updater(lambda l: l.next_to(m, LEFT))
self.play(ShowCreation(m), ShowCreation(m_label))
self.wait()
sub4 = CText('连接相应的点')
sub4.scale(0.3)
sub4.to_edge(RIGHT)
self.play(FadeOut(sub3))
self.play(Write(sub4))
ma = Line()
ma.add_updater(lambda l:\
l.put_start_and_end_on(
m.get_center(),
a.get_center()
))
af = Line(a.get_center(), focus.get_center() + RIGHT)
mf = Line()
mf.add_updater(lambda l:\
l.put_start_and_end_on(
m.get_center(),
focus.get_center()
))
self.play(*[ShowCreation(e) for e in [af, mf, ma]])
self.wait()
sub5 = CText('延长MA, MF')
sub5.scale(0.3)
sub5.to_edge(RIGHT)
self.play(FadeOut(sub4))
self.play(Write(sub5))
def get_ma_extent():
vec = a.get_center() - m.get_center()
vec *= FRAME_WIDTH
return a.get_center() + vec
ma_extent = Line()
ma_extent.add_updater(lambda l:\
l.put_start_and_end_on(
a.get_center(),
get_ma_extent()
))
def get_mf_extent():
vec = focus.get_center() - m.get_center()
return focus.get_center() + normalize(vec)
mf_extent = Line()
mf_extent.add_updater(lambda l:\
l.put_start_and_end_on(
focus.get_center(),
get_mf_extent()
))
self.play(ShowCreation(mf_extent), ShowCreation(ma_extent))
self.wait()
sub6 = CText('做对称线(相等的角)')
sub6.scale(0.3)
sub6.to_edge(RIGHT)
self.play(FadeOut(sub5))
self.play(Write(sub6))
def get_flip():
loc = get_mf_extent()
f = focus.get_center()
x = loc[0] - f[0]
y = loc[1] - f[1]
ang = 2 * np.arctan2(y, x)
vec = np.cos(ang) * RIGHT + np.sin(ang) * UP
return vec
mf_flip = Line()
mf_flip.add_updater(lambda l:\
l.put_start_and_end_on(
focus.get_center(),
get_flip() + focus.get_center()
))
self.play(ShowCreation(mf_flip))
sub7 = CText('交MA于点P')
sub7.scale(0.3)
sub7.to_edge(RIGHT)
self.play(FadeOut(sub6))
self.play(Write(sub7))
mf_flip_extent = Line()
mf_flip_extent.add_updater(lambda l:\
l.put_start_and_end_on(
focus.get_center(),
get_flip() * FRAME_WIDTH\
+ focus.get_center()
))
self.play(ShowCreation(mf_flip_extent))
def get_p():
x1 = m.get_center()[0]
y1 = m.get_center()[1]
x2 = a.get_center()[0]
y2 = a.get_center()[1]
x3 = focus.get_center()[0]
y3 = focus.get_center()[1]
vec = get_flip()
x4 = x3 + vec[0]
y4 = y3 + vec[1]
a1 = y2 - y1
b1 = x1 - x2
c1 = a1 * x1 + b1 * y1
a2 = y4 - y3
b2 = x3 - x4
c2 = a2 * x3 + b2 * y3
determinant = a1 * b2 - a2 * b1
if determinant == 0:
return a.get_center()
x = (b2 * c1 - b1 * c2) / determinant
y = (a1 * c2 - a2 * c1) / determinant
return x * RIGHT + y * UP
p = Dot()
p.set_fill(DARK_BLUE)
p.plot_depth = 1
p.add_updater(lambda m: m.move_to(get_p()))
p_label = TexMobject('P').scale(0.5)
p_label.add_updater(lambda m:\
m.next_to(p, RIGHT, buff=SMALL_BUFF))
self.play(ShowCreation(p), ShowCreation(p_label))
self.wait(3)
self.play(ApplyMethod(y_val.set_value, -4))
graph = self.get_graph(color=LIGHT_BROWN)
self.play(ShowCreation(graph))
self.wait(3)
self.play(ApplyMethod(y_val.set_value, -8))
self.wait(3)
self.play(ApplyMethod(y_val.set_value, -6))
self.wait(3)
self.play(ApplyMethod(y_val.set_value, 6))
self.wait(3)
self.play(ApplyMethod(y_val.set_value, 8))
self.wait(10)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
focus = Dot(self.get_focus()).set_fill(DARK_BLUE)
directrix = self.get_directrix()
focusLabel = TexMobject('F').scale(0.75)
focusLabel.next_to(focus, RIGHT, buff=SMALL_BUFF)
self.directrix = directrix
focus.plot_depth = 1
sub1 = CText('在抛物线上任取不同的两点P1,P2').scale(0.4)
sub1.to_corner(RIGHT + DOWN)
p1_y = ValueTracker(7)
p2_y = ValueTracker(2)
p1 = Dot()
p1.add_updater(
lambda m: m.move_to(self.value_to_point(p1_y.get_value())))
p1.plot_depth = 1
p2 = Dot()
p2.add_updater(
lambda m: m.move_to(self.value_to_point(p2_y.get_value())))
p2.plot_depth = 1
p1.set_fill(RED)
p2.set_fill(RED)
p1Label = TexMobject('P_1').scale(0.75)
p2Label = TexMobject('P_2').scale(0.75)
p1Label.add_updater(lambda m:\
m.next_to(p1, RIGHT, buff=SMALL_BUFF))
p2Label.add_updater(lambda m:\
m.next_to(p2, LEFT+UP, buff=SMALL_BUFF))
sub2 = CText('连接两点，延长交准线于点K')
sub2.scale(0.4).to_corner(RIGHT + DOWN)
ppLine = Line()
ppLine.add_updater(lambda m:\
m.put_start_and_end_on(p1.get_center(),\
self.get_directrix_point(p1, p2)))
k = Dot()
k.plot_depth = 1
k.set_fill(DARK_BLUE)
k.add_updater(lambda m: m.move_to(ppLine.points[-1]))
kLabel = TexMobject('K').scale(0.75)
kLabel.add_updater(lambda m:\
m.next_to(k, LEFT, buff=SMALL_BUFF))
sub3 = CText('分别连接P1F, P2F')
sub3.scale(0.4).to_corner(RIGHT + DOWN)
p1f = Line()
p2f = Line()
p1f.add_updater(lambda m:\
m.put_start_and_end_on(p1.get_center(),\
focus.get_center()))
p2f.add_updater(lambda m:\
m.put_start_and_end_on(p2.get_center(),\
focus.get_center()))
sub4 = CText('延长P1F交准线于D')
sub4.scale(0.4).to_corner(RIGHT + DOWN)
p1fd = Line()
p1fd.add_updater(lambda m:\
m.put_start_and_end_on(\
focus.get_center(),\
self.get_directrix_point(p1, focus)))
d = Dot()
d.plot_depth = 1
d.set_fill(DARK_BLUE)
d.add_updater(lambda m: m.move_to(p1fd.points[-1]))
dLabel = TexMobject('D')
dLabel.scale(0.75)
dLabel.add_updater(lambda m:\
m.next_to(d, LEFT, buff=SMALL_BUFF))
sub5 = CText('连接KF')
sub5.scale(0.4).to_corner(RIGHT + DOWN)
kf = Line()
kf.add_updater(lambda m:\
m.put_start_and_end_on\
(k.get_center(), focus.get_center()))
ang1 = ArcBetweenPoints(*self.get_arc_point(
p2.get_center(), focus.get_center(), k.get_center()))
ang1.add_updater(lambda m:\
m.put_start_and_end_on(
*self.get_arc_point(
p2.get_center(),
focus.get_center(),
k.get_center()
)))
ang1Label = TexMobject('1').scale(0.5)
ang1Label.add_updater(lambda m:\
m.move_to(ang1.get_center()))
ang2 = ArcBetweenPoints(*self.get_arc_point(
k.get_center(), focus.get_center(), d.get_center()))
ang2.add_updater(lambda m:\
m.put_start_and_end_on(
*self.get_arc_point(
k.get_center(),
focus.get_center(),
d.get_center()
)))
ang2Label = TexMobject('2').scale(0.5)
ang2Label.add_updater(lambda m:\
m.move_to(ang2.get_center()))
ang1Value = DecimalNumber(self.get_angle(
p2.get_center(), focus.get_center(), k.get_center()) / DEGREES,
num_decimal_places=2)
ang1Value.add_updater(lambda m:\
m.set_value(self.get_angle(
p2.get_center(),
focus.get_center(),
k.get_center()
) / DEGREES))
ang2Value = DecimalNumber(self.get_angle(
k.get_center(), focus.get_center(), d.get_center()) / DEGREES,
num_decimal_places=2)
ang2Value.add_updater(lambda m:\
m.set_value(self.get_angle(
k.get_center(),
focus.get_center(),
d.get_center()
) / DEGREES))
ang1Tail = TexMobject('^{\circ}')
ang2Tail = TexMobject('^{\circ}')
ang1head = TexMobject('\\angle 1=')
ang1Text = VGroup(ang1head, ang1Value, ang1Tail)
ang1Text.arrange(buff=SMALL_BUFF)
ang1Tail.shift(0.15 * UP)
ang2head = TexMobject('\\angle 2=')
ang2Text = VGroup(ang2head, ang2Value, ang2Tail)
ang2Text.arrange(buff=SMALL_BUFF)
ang2Tail.shift(0.15 * UP)
angs = VGroup(ang1Text, ang2Text)
angs.arrange(buff=MED_SMALL_BUFF)
angs.shift(3 * RIGHT + 2 * UP)
m1 = Dot()
m1.plot_depth = 1
m1.set_fill(ORANGE)
m1.add_updater(lambda m:\
m.move_to(self.coords_to_point(
-self.focus, p1_y.get_value()
)))
m2 = Dot()
m2.plot_depth = 1
m2.set_fill(ORANGE)
m2.add_updater(lambda m:\
m.move_to(self.coords_to_point(
-self.focus, p2_y.get_value()
)))
m1Label = TexMobject('M_1').scale(0.75)
m2Label = TexMobject('M_2').scale(0.75)
m1Label.add_updater(lambda m:\
m.next_to(m1, LEFT, buff=SMALL_BUFF))
m2Label.add_updater(lambda m:\
m.next_to(m2, LEFT, buff=SMALL_BUFF))
m1p1 = DashedLine()
m1p1.add_updater(lambda m:\
m.put_start_and_end_on(
m1.get_center(), p1.get_center()
))
m2p2 = DashedLine()
m2p2.add_updater(lambda m:\
m.put_start_and_end_on(
m2.get_center(), p2.get_center()
))
fracs = TexMobject('{KP_2', '\\over', 'KP_1}', '=', '{M_2P_2',
'\\over', 'M_1P_1}', '=', '{FP_2', '\\over',
'FP_1}')
fracs.shift(3 * RIGHT + 2 * UP)
fracs2 = TexMobject('{KP_2', '\\over', 'KP_1}', '=', '{FP_2', '\\over',
'FP_1}')
fracs2.move_to(fracs.get_center())
fracs2.align_to(fracs, LEFT)
fracs3 = TexMobject('{KP_2', '\\over', 'FP_2}', '=', '{KP_1', '\\over',
'FP_1}')
fracs3.move_to(fracs2.get_center())
explain = CText('由正弦定理').scale(0.4)
explain.next_to(fracs3, DOWN)
explain.align_to(fracs3, LEFT)
fracs4 = TexMobject('{\\sin\\angle 1', '\\over', '\\sin\\angle K}',
'=', '{\\sin\\angle KFP_1', '\\over',
'\\sin\\angle K}')
fracs4.next_to(explain, DOWN)
fracs4.align_to(explain, LEFT)
form = TexMobject('\\sin \\angle 1 = \\sin \\angle KFP_1')
form.next_to(fracs4, DOWN)
form.align_to(fracs4, LEFT)
form2 = TexMobject('\\angle1 < \\angle KFP_1 < \\pi')
form2.next_to(form, DOWN)
form2.align_to(form, LEFT)
form3 = TexMobject('\\angle1 = \pi - \\angle KFP_1 = \\angle 2')
form3.next_to(form2, DOWN)
form3.align_to(form2, LEFT)
remover = Rectangle(height=FRAME_HEIGHT, width=FRAME_WIDTH)
remover.set_color(BLACK)
remover.set_fill(BLACK, opacity=1)
remover.plot_depth = 2
# kp2 = Line()
# kp2.add_updater(lambda m:\
# m.put_start_and_end_on(k.get_center(),
# p2.get_center()))
# kp2.set_color(YELLOW)
############################################
# Animation part #
############################################
self.play(ShowCreation(focus), ShowCreation(directrix))
self.play(ShowCreation(graph), Write(focusLabel))
self.play(Write(sub1))
self.play(*[ShowCreation(e) for e in\
[p1, p2, p1Label, p2Label]])
self.wait()
self.play(FadeOut(sub1))
self.play(Write(sub2))
self.wait()
self.play(ShowCreation(ppLine))
self.play(ShowCreation(k), Write(kLabel))
self.wait()
self.play(FadeOut(sub2))
self.play(Write(sub3))
self.play(*[ShowCreation(e) for e in [p1f, p2f]])
self.wait()
self.play(FadeOut(sub3))
self.play(Write(sub4))
self.play(ShowCreation(p1fd))
self.play(*[ShowCreation(e) for e in [d, dLabel]])
self.wait()
self.play(FadeOut(sub4))
self.play(Write(sub5))
self.wait()
self.play(ShowCreation(kf))
self.play(ShowCreation(ang1), Write(ang1Label))
self.play(ShowCreation(ang2), Write(ang2Label))
self.play(FadeOut(sub5))
self.play(Write(angs))
self.play(*[ShowCreation(e) for e in\
[m1, m2, m1p1, m2p2, m1Label, m2Label]])
self.play(ApplyMethod(p2_y.set_value, -1), run_time=2)
self.wait()
self.play(ApplyMethod(p1_y.set_value, 5))
self.wait()
self.play(ApplyMethod(p1_y.set_value, 9), run_time=3)
self.wait()
self.play(ApplyMethod(p2_y.set_value, 3), run_time=2)
self.play(FadeOut(angs))
self.wait()
self.play(Write(fracs))
self.wait(5)
#self.play(ReplacementTransform(fracs, fracs2))
self.play(FadeOut(fracs[4:8]))
self.play(*[
ApplyMethod(fracs[i].move_to, fracs[i - 4].get_center())
for i in range(8, 11)
])
# self.play(FadeOut(fracs), FadeIn(fracs2), run_time=0.1)
# self.wait(5)
# self.play(ReplacementTransform(fracs2, fracs3))
self.wait(5)
pos1 = fracs[2].get_center()
pos2 = fracs[8].get_center()
self.play(ApplyMethod(fracs[2].move_to, pos2),
ApplyMethod(fracs[8].move_to, pos1))
self.wait(5)
self.play(Write(explain))
self.wait(3)
self.play(ShowCreationThenDestruction(
Polygon(k.get_center(), focus.get_center(),
p2.get_center()).set_fill(DARK_BLUE, opacity=1)),
run_time=3)
self.play(Write(fracs4[:3]))
self.play(ShowCreationThenDestruction(
Polygon(k.get_center(), focus.get_center(),
p1.get_center()).set_fill(DARK_BLUE, opacity=1)),
run_time=3)
self.play(Write(fracs4[3:]))
self.wait(3)
self.play(Write(form))
self.wait(3)
self.play(Write(form2))
self.wait(3)
self.play(Write(form3))
self.wait(5)
self.play(FadeIn(remover))
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focusLabel = TexMobject('F').scale(0.5)
focusLabel.next_to(focus, RIGHT + UP)
self.play(*[ShowCreation(e) for\
e in [graph, directrix, focus, focusLabel]])
h_line = self.get_horizontal()
x = Dot()
x.set_fill(DARK_BROWN)
x.plot_depth = 1
x.move_to(self.coords_to_point(-self.focus, 0))
x_label = TexMobject('X').scale(0.5)
x_label.next_to(x, LEFT + UP)
self.play(ShowCreation(h_line))
self.play(ShowCreation(x), ShowCreation(x_label))
y_val = ValueTracker(8)
p = Dot()
p.set_fill(DARK_BLUE)
p.plot_depth = 1
p.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()),
y_val.get_value()
)))
q = Dot()
q.set_fill(DARK_BLUE)
q.plot_depth = 1
q.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(-y_val.get_value()),
-y_val.get_value()
)))
t = Dot()
t.set_fill(DARK_BLUE)
t.plot_depth = 1
t.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()), 0
)))
p_label = TexMobject('P').scale(0.5)
p_label.add_updater(lambda m:\
m.next_to(p, RIGHT))
q_label = TexMobject('Q').scale(0.5)
q_label.add_updater(lambda m:\
m.next_to(q, RIGHT))
t_label = TexMobject('T').scale(0.5)
t_label.add_updater(lambda m:\
m.next_to(t, RIGHT + UP))
pq = Line()
pq.add_updater(lambda m:\
m.put_start_and_end_on(
p.get_center(),
self.coords_to_point(
self.func(-y_val.get_value()),
-y_val.get_value()
)))
pt = Line()
pt.add_updater(lambda m:\
m.put_start_and_end_on(
p.get_center(),
self.coords_to_point(
self.func(y_val.get_value()), 0
)))
self.play(ShowCreation(p), ShowCreation(p_label))
self.play(ShowCreation(pt))
self.play(ShowCreation(t), ShowCreation(t_label))
label1 = CText('纵标线').scale(0.3)\
.next_to(pt, RIGHT)
self.play(ShowCreation(label1))
self.wait()
self.play(FadeOut(label1))
self.play(ShowCreation(pq))
self.remove(pt)
self.play(ShowCreation(q), ShowCreation(q_label))
label2 = CText('双纵标线').scale(0.3)\
.next_to(t, RIGHT+DOWN)
self.play(ShowCreation(label2))
self.wait()
self.play(FadeOut(label2))
self.wait()
inter = Dot()
inter.set_fill(DARK_BLUE)
inter.plot_depth = 1
inter.add_updater(lambda m:\
m.move_to(
self.coords_to_point(
4*(self.focus**3)/(y_val.get_value()**2),
4*self.focus**2/y_val.get_value()
) if y_val.get_value() != 0 else
self.coords_to_point(0, 0)
))
inter_label = TexMobject("P'").scale(0.5)
inter_label.add_updater(lambda m:\
m.next_to(inter, LEFT + UP, buff=SMALL_BUFF))
px = Line()
px.add_updater(lambda m:\
m.put_start_and_end_on(
self.right(p, inter),
x.get_center()
))
self.play(ShowCreation(px))
self.play(ShowCreation(inter),
ShowCreation(inter_label))
self.wait()
form = CText("P'Q经过焦点").shift(UP)
form.scale(0.5)
form.to_edge(RIGHT)
self.play(Write(form))
interq = Line()
interq.add_updater(lambda m:\
m.put_start_and_end_on(
inter.get_center(),
q.get_center()
))
self.play(ShowCreation(interq))
self.wait(2)
self.play(ApplyMethod(y_val.set_value, 4))
self.wait(2)
self.play(ApplyMethod(y_val.set_value, -4))
self.wait(2)
self.play(ApplyMethod(y_val.set_value, -9))
self.wait(2)
self.play(ApplyMethod(y_val.set_value, 9))
self.wait(10)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focusLabel = TexMobject('F').scale(0.7)
focusLabel.next_to(focus, RIGHT)
self.play(*[ShowCreation(e) for\
e in [graph, directrix, focus, focusLabel]])
y_val = ValueTracker(8)
p1 = Dot()
p1.set_color(DARK_BLUE)
p1.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()),
y_val.get_value()
)))
p1.plot_depth = 1
p1Label = TexMobject('P_1').scale(0.7)
p1Label.add_updater(lambda m:\
m.next_to(p1, RIGHT, buff=SMALL_BUFF))
p2 = Dot()
p2.set_color(DARK_BLUE)
p2.add_updater(lambda m:\
m.move_to(self.get_opposite(p1)))
p2.plot_depth = 1
p2Label = TexMobject('P_2').scale(0.7)
p2Label.add_updater(lambda m:\
m.next_to(p2, RIGHT, buff=SMALL_BUFF))
focus_chord = Line()
focus_chord.add_updater(lambda m:\
m.put_start_and_end_on(
p1.get_center(),
self.get_opposite(p1)
))
self.play(ShowCreation(p1), ShowCreation(p1Label))
self.play(ShowCreation(focus_chord))
self.play(ShowCreation(p2), ShowCreation(p2Label))
fc_def = CText('焦点弦')
fc_def.move_to(focus_chord.get_center())
fc_def.shift(0.2 * RIGHT + 0.1 * DOWN)
self.play(Write(fc_def))
self.wait(2)
self.play(FadeOut(fc_def))
q_y = ValueTracker(2)
q = Dot()
q.set_fill(DARK_BLUE)
q.plot_depth = 1
q.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(q_y.get_value()),
q_y.get_value()
)))
qLabel = TexMobject('Q').scale(0.7)
qLabel.add_updater(lambda m:\
m.next_to(q, LEFT, buff=SMALL_BUFF))
k1 = Dot()
k1.set_fill(BLUE_E)
k1.plot_depth = 1
k1.add_updater(lambda m:\
m.move_to(self.chord_to_directrix(p1, q)))
k1Label = TexMobject('K_1').scale(0.7)
k1Label.add_updater(lambda m:\
m.next_to(k1, LEFT, buff=SMALL_BUFF))
k2 = Dot()
k2.set_fill(BLUE_E)
k2.plot_depth = 1
k2.add_updater(lambda m:\
m.move_to(self.chord_to_directrix(p2, q)))
k2Label = TexMobject('K_2').scale(0.7)
k2Label.add_updater(lambda m:\
m.next_to(k2, LEFT, buff=SMALL_BUFF))
l1 = Line()
l1.add_updater(lambda m:\
m.put_start_and_end_on(
self.right(p1, q),
self.chord_to_directrix(p1, q)
))
l2 = Line()
l2.add_updater(lambda m:\
m.put_start_and_end_on(
self.right(p2, q),
self.chord_to_directrix(p2, q)
))
self.play(ShowCreation(q), ShowCreation(qLabel))
self.play(ShowCreation(l1), ShowCreation(l2))
self.play(*[ShowCreation(e) for e in [k1, k2, k1Label, k2Label]])
k1f = Line()
k1f.add_updater(lambda m:\
m.put_start_and_end_on(
k1.get_center(), focus.get_center()
))
k2f = Line()
k2f.add_updater(lambda m:\
m.put_start_and_end_on(
k2.get_center(), focus.get_center()
))
self.play(ShowCreation(k1f), ShowCreation(k2f))
self.wait(1)
self.play(ApplyMethod(y_val.set_value,
5))
summary = TexMobject('K_1F \\perp K_2F').scale(2)
summary.to_edge(RIGHT)
self.wait(1)
self.play(Write(summary))
self.wait(5)
qf = Line()
qf.add_updater(lambda m:\
m.put_start_and_end_on(q.get_center(),
focus.get_center()))
self.play(ShowCreation(qf))
self.wait(1)
self.play(ApplyMethod(q_y.set_value,
-1))
self.wait(1)
self.play(ApplyMethod(y_val.set_value,
0.5))
self.wait(1)
self.play(ApplyMethod(y_val.set_value,
3),
ApplyMethod(q_y.set_value, 0.5))
self.wait(10)
def construct(self):
self.adjust_x_range()
lineCText = CText('设有一固定直线l')
directrix = self.get_directrix()
self.play(Write(lineCText))
self.play(ApplyMethod(lineCText.scale, 0.3), ShowCreation(directrix))
self.play(
ApplyMethod(lineCText.move_to,
self.coords_to_point(-self.focus + 3,
self.y_max - 2)), )
self.wait()
focusCText = CText('有一固定点F')
focus = Circle()\
.move_to(self.get_focus())\
.scale(0.1)\
.set_fill(ORANGE, opacity=1)
self.play(Write(focusCText))
self.wait()
self.play(ApplyMethod(focusCText.scale, 0.3))
self.play(
ApplyMethod(focusCText.move_to,
self.coords_to_point(self.focus + 3, 0)),
ShowCreation(focus))
self.wait()
question = CText('求到直线距离l与到\n点P距离相等的点的轨迹')
question.scale(0.4)
question.to_edge(RIGHT)
self.play(Write(question))
self.wait()
pickPoint = CText('在l上任取一点P')
pickPoint.scale(0.4)
pickPoint.to_edge(DOWN)
self.play(Write(pickPoint))
y = ValueTracker(5)
point = Circle()\
.scale(0.1)\
.set_fill(ORANGE, opacity=1)\
.move_to(self.coords_to_point(-self.focus, y.get_value()))
self.play(ShowCreation(point))
self.wait()
self.play(FadeOut(pickPoint))
connect = CText('连接FP')
connect.scale((0.4))
connect.to_edge(DOWN)
fp = DashedLine(point.get_center(), focus.get_center())
self.play(Write(connect))
self.play(ShowCreation(fp))
self.wait()
midRight = CText('做FP中垂线')
midRight.scale(0.4)
midRight.to_edge(DOWN)
midPoint = Circle()\
.scale(0.1)\
.move_to((point.get_center() + focus.get_center())/2)\
.set_fill(DARK_BLUE, opacity=1).set_color(DARK_BLUE)
midRightLine = DashedLine(LEFT * FRAME_WIDTH, RIGHT * FRAME_WIDTH)
midRightLine.rotate(fp.get_angle() + np.pi / 2,
about_point=midRight.get_center())
midRightLine.move_to(midPoint.get_center())
self.play(FadeOut(connect))
self.play(Write(midRight))
self.play(ShowCreation(midPoint))
self.play(ShowCreation(midRightLine))
self.wait()
right = CText('过P点做l的垂线')
right.scale(0.4)
right.to_edge(DOWN)
rightLine = DashedLine(LEFT * FRAME_WIDTH, RIGHT * FRAME_WIDTH)
rightLine.shift(UP * (point.get_center()[1]))
self.play(FadeOut(midRight))
self.play(Write(right))
self.play(ShowCreation(rightLine))
targetCText = CText('垂线与中垂线交点即为曲线上的点')
targetCText.scale(0.4).to_edge(DOWN)
target = Circle()\
.scale(0.1)\
.set_fill(RED, opacity=1)\
.set_color(ORANGE)\
.move_to(self.value_to_point(y.get_value()))
self.play(FadeOut(right))
self.play(Write(targetCText))
self.play(DrawBorderThenFill(target))
point.add_updater(lambda m: m.move_to(
self.coords_to_point(-self.focus, y.get_value())))
fp.add_updater(lambda m: m.put_start_and_end_on(
point.get_center(), focus.get_center()))
midPoint.add_updater(lambda m: m.move_to(
(point.get_center() + focus.get_center()) / 2))
rightLine.add_updater(lambda m: m.move_to(point.get_center()))
target.add_updater(
lambda m: m.move_to(self.value_to_point(y.get_value())))
def setRight(line):
line.put_start_and_end_on(LEFT * FRAME_WIDTH, RIGHT * FRAME_WIDTH)
line.rotate(fp.get_angle() + np.pi / 2,
about_point=midRight.get_center())
line.move_to(midPoint.get_center())
midRightLine.add_updater(setRight)
self.play(ApplyMethod(y.set_value, -2))
graph = self.get_graph(color=LIGHT_BROWN)
self.play(ApplyMethod(y.set_value, -8), ShowCreation(graph))
self.wait()
self.play(ApplyMethod(y.set_value, 8, run_time=2))
self.wait()
self.play(ApplyMethod(y.set_value, 2, run_time=2))
directDef = CText('直线l称为准线')
directDef.scale(0.4)
directDef.to_edge(DOWN)
dire = CText('准线')
dire.scale(0.3).move_to(lineCText.get_center())
dire.align_to(lineCText, LEFT)
self.play(FadeOut(targetCText))
self.play(Write(directDef))
self.play(Transform(lineCText, dire))
self.wait()
self.play(FadeOut(directDef))
focDef = CText('点F称为焦点')
focDef.scale(0.4).to_edge(DOWN)
foc = CText('焦点')
foc.scale(0.3).move_to(focusCText.get_center())\
.align_to(focusCText, LEFT)
self.play(Write(focDef))
self.play(Transform(focusCText, foc))
self.wait(3)
self.play(ShowCreation(self.get_horizontal()))
self.play(Write(CText('轴')\
.scale(0.3).move_to(self.coords_to_point(5, 0.5))))
self.play(ShowCreation(
Circle()\
.scale(0.1)\
.set_color(DARK_BLUE)\
.set_fill(DARK_BLUE, opacity=1)\
.move_to(self.coords_to_point(0, 0))
))
self.play(Write(CText('顶点')\
.scale(0.3).move_to(self.coords_to_point(0.5, 0.5))))
self.wait(3)
def construct(self):
self.adjust_x_range()
graph = self.get_graph(color=LIGHT_BROWN)
directrix = self.get_directrix()
focus = Dot().move_to(self.get_focus())
focus.set_fill(DARK_BROWN)
focus.plot_depth = 1
focusLabel = TexMobject('F').scale(0.5)
focusLabel.next_to(focus, DOWN, buff=SMALL_BUFF)
self.play(*[ShowCreation(e) for\
e in [graph, directrix, focus, focusLabel]])
y_val = ValueTracker(8)
p1 = Dot()
p1.set_color(DARK_BLUE)
p1.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()),
y_val.get_value()
)))
p1.plot_depth = 1
p1_label = TexMobject('P_1').scale(0.5)
p1_label.plot_depth = 1
p1_label.add_updater(lambda m:\
m.next_to(p1, RIGHT, buff=SMALL_BUFF))
p2 = Dot()
p2.plot_depth = 1
p2.set_color(DARK_BLUE)
p2.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(-y_val.get_value()),
-y_val.get_value()
)))
p2_label = TexMobject('P_2').scale(0.5)
p2_label.plot_depth = 1
p2_label.add_updater(lambda m:\
m.next_to(p2, RIGHT, buff=SMALL_BUFF))
a = Dot()
a.set_color(DARK_BLUE)
a.plot_depth = 1
a.move_to(self.coords_to_point(0, 0))
a_label = TexMobject('A').scale(0.5)
a_label.next_to(a, DL, buff=SMALL_BUFF)
h_line = Line(LEFT*6, RIGHT*2)
self.play(*[ShowCreation(e) for e in\
[h_line, a, a_label]])
self.wait()
sub1 = CText('取任意双纵标线P1P2')\
.scale(0.3).to_edge(RIGHT)
self.play(Write(sub1))
self.wait()
self.play(*[ShowCreation(e) for e in\
[p1, p1_label, p2, p2_label]])
p1p2 = Line()
p1p2.add_updater(lambda l:\
l.put_start_and_end_on(
p1.get_center(), p2.get_center()
))
self.play(ShowCreation(p1p2))
self.wait()
n = Dot()
n.set_color(DARK_BLUE)
n.plot_depth = 1
n.add_updater(lambda m:\
m.move_to(self.coords_to_point(
self.func(y_val.get_value()), 0
)))
n_label = TexMobject('N').scale(0.5)
n_label.plot_depth = 1
n_label.add_updater(lambda m:\
m.next_to(n, DR, buff=SMALL_BUFF))
self.play(
ShowCreation(n),
ShowCreation(n_label)
)
self.wait()
sub2 = CText('做P1、P2、A的外接圆')\
.scale(0.3).to_edge(RIGHT)
self.play(FadeOut(sub1))
self.play(Write(sub2))
def set_circle(c):
pos1 = a.get_center()
pos2 = p1.get_center()
pos3 = p2.get_center()
p = self.focus
y = y_val.get_value()
o = self.coords_to_point(
(16*p*p+y*y)/(8*p), 0
)
r = o[0] - pos1[0]
c.move_to(o)
c.stretch_to_fit_height(2 * r)
c.stretch_to_fit_width(2 * r)
circle = Circle()
circle.set_color(MAROON_E)
circle.add_updater(lambda m: set_circle(m))
self.play(ShowCreation(circle))
self.wait()
sub3 = CText('交轴于点Q')\
.scale(0.3).to_edge(RIGHT)
self.play(FadeOut(sub2))
self.play(Write(sub3))
q = Dot()
q.set_fill(DARK_BLUE)
q.plot_depth = 1
q.add_updater(lambda m:\
m.move_to(n.get_center() +\
4 * (focus.get_center() - a.get_center())))
q_label = TexMobject('Q').scale(0.5)
q_label.plot_depth = 1
q_label.add_updater(lambda m:\
m.next_to(q, DR, buff=SMALL_BUFF))
self.play(
ShowCreation(q),
ShowCreation(q_label)
)
self.wait()
corollary = VGroup()
head = CText('推论：').scale(0.25)
head.set_fill(DARK_BLUE)
crlly = TexMobject('NQ=4AF').scale(0.5)
head_line = VGroup(head, crlly)
head_line.arrange(RIGHT)
proof = VGroup()
proof_head = CText('证明：').scale(0.25)
proof_head.set_fill(DARK_BLUE)
proof.add(proof_head)
proof_details = VGroup()
prf1 = CText('在直角三角形AQP1中')\
.scale(0.25)
prf2 = TexMobject('P_1N^2=AN\\cdot NQ')\
.scale(0.5)
prf3 = VGroup()
prf3_1 = CText('又').scale(0.25)
prf3_2 = TexMobject(
'\\because P_1N^2=4AF\\cdot AN')\
.scale(0.5)
prf3.add(prf3_1, prf3_2)
prf3.arrange(RIGHT, buff=SMALL_BUFF)
prf4 = TexMobject(
'\\therefore AN\\cdot NQ=4AF\\cdot AN'
).scale(0.5)
prf5 = TexMobject(
'\\therefore NQ=4AF'
).scale(0.5)
proof_details.add(prf1, prf2, prf3,
prf4, prf5)
proof_details.arrange(DOWN)
proof.add(proof_details)
proof.arrange(RIGHT)
proof_details.align_to(proof_head, UP)
for e in [prf2, prf3, prf4, prf5]:
e.align_to(prf1, LEFT)
corollary.add(head_line)
corollary.add(proof)
corollary.arrange(DOWN)
head_line.align_to(proof, LEFT)
corollary.to_edge(RIGHT)
self.play(FadeOut(sub3))
self.play(ShowCreation(head_line))
self.play(Write(proof_head))
self.wait(5)
self.play(Write(prf1))
ap1 = DashedLine()
ap1.add_updater(lambda l:\
l.put_start_and_end_on(
a.get_center(), p1.get_center()
))
qp1 = DashedLine()
qp1.add_updater(lambda l:\
l.put_start_and_end_on(
q.get_center(), p1.get_center()
))
self.play(
ShowCreation(ap1),
ShowCreation(qp1)
)
self.play(ShowCreationThenDestruction(
Polygon(
a.get_center(),
q.get_center(),
p1.get_center()
).set_fill(ORANGE, opacity=1)
))
self.wait(5)
self.play(Write(prf2))
self.wait(5)
self.play(Write(prf3))
self.wait(3)
self.play(Write(prf4))
self.wait(3)
self.play(Write(prf5))
self.wait(5)
self.play(y_val.set_value, 4)
self.wait(3)
self.play(y_val.set_value, 2)
self.wait(10)