雙曲線的光學性質
Author: 藍邦偉  老師

雙曲線的光學性質

c>a，拉動P點觀察

a = 3 (slider from 1 to 10, step 1)
O: (x((3.0 * Corner[1.0] + 5.0 * Corner[2.0]) / 8.0), y((Corner[1.0] + Corner[4.0]) / 2.0))
A_1: O + a * (1.0, 0.0)
A_2: O - a * (1.0, 0.0)
c = 5 (slider from 1 to 10, step 1)
d: (x - x(O))^(2.0) / a^(2.0) - (y - y(O))^(2.0) / (c^(2.0) - a^(2.0)) = 1.0
P = Point(d)
F_1: O + c * (1.0, 0.0)
F_2: O - c * (1.0, 0.0)
b = Segment(P, F_1)
e = Segment(P, F_2)
f, g = AngularBisector(e, b)
α = Angle(b, f)
β = Angle(f, e)
h = Line(A_1, A_2)
i = Ray(F_2, P)
j = Ray(F_1, P)
T_1 = Corner(1.0)
T_4 = Corner(4.0)
T_2: (3.0 * Corner[1.0] + Corner[2.0]) / 4.0
T_3: (3.0 * Corner[4.0] + Corner[3.0]) / 4.0
k = Segment(T_2, T_3)
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)