雙曲線與直線的關係
Author: 藍邦偉  老師

雙曲線與直線

c²=a+b²

\frac{x²}{a²}-\frac{y²}{b²}=1

k = 0 (slider from -20 to 20, step 1)
h = 0 (slider from -20 to 20, step 1)
b = 3 (slider from 0 to 36, step 0.5)
a = 4 (slider from 0 to 36, step 1)
Γ: (x - h)^(2) / a^(2) - (y - k)^(2) / b^(2) = 1
d: x = h
e: y = k
M: (h, k)
A_1: (h + a, k)
A', A_2 = Intersect(Γ, e)
B, B' = Intersect(Γ, d)
f = Segment(A', A_2)
g = Segment(B, B')
F: (h + (a^(2) + b^(2))^(1 / 2), k)
F': (h - (a^(2) + b^(2))^(1 / 2), k)
i = OrthogonalLine(F, f)
j = OrthogonalLine(F', f)
A_3, C = Intersect(Γ, i)
D, E = Intersect(Γ, j)
K_1: (x(Corner[1]), 0)
K_2: (x(Corner[2]), 0)
K_3: (0, y(Corner[2]))
K_4: (0, y(Corner[3]))
u = Vector(K_1, K_2)
v = Vector(K_3, K_4)
t_5 = 4.1 (slider from 4 to 5, step 0.1)
c: sqrt(a^(2) - b^(2))
s = Segment(A_2, F)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3 * Corner[1] + Corner[2]) / 4
T_3: (3 * Corner[4] + Corner[3]) / 4
多邊形2, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
r = Segment(T_3, T_2)
a_1 = LineBisector(M, A_2)
b_1 = LineBisector(M, B)
J = Point(b_1)
c_1 = LineBisector(M, F)
I = Point(c_1)
q = LineBisector(M, A_2)
K = Point(q)
H_1 = (4, 3)
H_2 = (-4, 3)
H_3 = (-4, -3)
H_4 = (4, -3)
i_1 = Segment(H_2, H_3)
j_1 = Segment(H_3, H_4)
k_1 = Segment(H_4, H_1)
l_1 = Segment(H_1, H_2)
O = (0, 0)
α = 2.443460952792061 rad (slider from 2.443460952792061 to 3.839724354387525, step 0.1*°)
β = 0 rad (slider from 0 to 6.283185307179586, step 0.1*°)
n = 0 (slider from 0 to 5, step 1)
L_a: y = tan(α) * x
G, H = Intersect(Γ, L_a)
t = -120 (slider from -120 to 120, step 0.1)
L = (-9.316539736691814, 5.54654147111633)
A = (10.579617948580204, -3.757417158687131)
l = Line(L, A)
m: 3 * x - 4 * y = t
p: 3 * x + 4 * y = t
P: (4 / cos(β), 3 * tan(β))
d_1, e_1 = Tangent(P, Γ)