雙曲線的性質(3)
Author: 藍邦偉  老師

c²=a²+b²

$M$

$A'$

$A$

$F$

$F'$

雙曲線的性質

$B$

$b$

$c$

Γ:\frac{x²}{a²}-\frac{y²}{b²}=1

c²=a²+b²

$a$

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 = Intersect(Γ, e)
f = Segment(A', A)
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 = 4.88 (slider from 4 to 5, step 0.01)
c: sqrt(a^(2) - b^(2))
s = Segment(A, F)
A_{a}: (h + t, k)
A_{b}: (h, k + (5 - t) * 3)
l = Segment(A_{b}, A_{a})
多邊形1, a_{a}, a_{b}, m = Polygon(A_{b}, M, A_{a})
n = LineBisector(A_{b}, A_{a})
G = Midpoint(A_{b}, A_{a})
p = Circle(G, A_{b})
H = Intersect(p, n, 1)
G' = Dilate(G, -0.2, H)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3.3 * Corner[1] + 0.7 * Corner[2]) / 4
T_3: (3.3 * Corner[4] + 0.7 * Corner[3]) / 4
多邊形2, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
a_1 = LineBisector(M, A)
B = (0, 3)
b_1 = LineBisector(M, B)
J: Point[b_1] + (1, 0)
d_1 = CircleArc(J, B, M)
c_1 = LineBisector(M, F)
I = Point(c_1)
q = LineBisector(M, A)
e_1 = LineBisector(A_{b}, A_{a})
K = Point(q)
g_1 = Circle(A_{b}, A_{a})
L, N = Intersect(g_1, e_1)
h_1 = CircleArc(L, A_{a}, A_{b})
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)
f_1 = CircleArc(K, M, A)