橢圓的準線
Author: 藍邦偉  老師

$ O $

      $ \frac{\overline{QF}}{\overline{QA}}=\frac{\overline{QA}}{d(Q,L)} $
$⇒\frac{c}{a}=\frac{a}{d(Q,L)}$
$⇒d(Q,L)=\frac{a²}{c}$

$ 橢圓的準線 $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
a = 4 (slider from 1 to 5, step 1)
b = 3 (slider from 1 to 5, step 1)
c: sqrt(a^(2) - b^(2))
h = 2 (slider from -5 to 5, step 1)
k = 2 (slider from -5 to 5, step 1)
Γ: (x - h)^(2) / a^(2) + (y - k)^(2) / b^(2) = 1
A: (h + a, k)
A': (h - a, k)
F: (h + c, k)
F': (h - c, k)
L: x = h + a^(2) / c
L': x = h - a^(2) / c
Q_A: (h, k)
B: (h, k + b)
B': (h, k - b)
d = Segment((x(Q_2), y(A)), (x(Corner[3]), y(A)))
e = Segment(B, B')
text4: "$ L:x=h±\frac{a^2}{c} $
            $=" + (LaTeX[h]) + "±" + (LaTeX[a * a / c]) + "$
$⇒L:x=" + (LaTeX[h + a * a / c]) + "$
     $L':x=" + (LaTeX[h - a * a / c]) + "$"
text2_1: "$ Γ:\frac{" + (LaTeX[If[h ≟ 0, "", "("]]) + "" + (LaTeX[If[h ≟ 0, "x^2", If[h > 0, "x-" * abs(h), "x+" * abs(h)]]]) + "" + (LaTeX[If[h ≟ 0, "", ")^2"]]) + "}{" + (LaTeX[a^(2)]) + "}+\frac{" + (LaTeX[If[k ≟ 0, "", "("]]) + "" + (LaTeX[If[k ≟ 0, "y^2", If[k > 0, "y-" * abs(h), "y+" * abs(k)]]]) + ")²}{" + (LaTeX[b^(2)]) + "}=1 $"