Hyperbola

Vertex

Vertex

TRANSVERSE AXIS

P(x,y)

n > 0

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MAJOR AXIS

TRANSVERSE AXIS

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a = 10.2 (slider from 0 to 20, step 0.01)
b = 16.1 (slider from 0 to 20, step 0.01)
c: x^(2) / a^(2) - y^(2) / b^(2) = 1
F_1, F_2 = Focus(c)
C, D, E, F = Vertex(c)
d = Segment(C, D)
C' = Translate(C, (0, b + 4))
D' = Translate(D, (0, b + 4))
G = Point(c)
e = Segment(G, F_1)
f = Segment(G, F_2)
g: e + f
C'_1 = Translate(C, (b + 4, 0))
h: x = x(C)
i: x = x(D)
j: y = y(C)
k: y = y(D)
n = 0 (slider from 0 to 4, step 0.01)
u = Vector(C, C')
v = Vector(D, D')
C'_2 = Dilate(C, If[0  <  n  <  1, 1 - n, 0], C')
D'_2 = Dilate(D, If[0  <  n  <  1, 1 - n, 0], D')
l = Segment(C'_2, D'_2)
A' = Dilate(F_1, If[1  <  n  <  2, 2 - n, 1], C')
w = Vector(F_1, A')
G' = Translate(G, w)
m = Segment(A', G')
p = Segment(C, D)
α = Angle(F_2, F_1, G)
A'' = Rotate(A', If[1  <  n  <  2, ((-(2 - n)) * α)], A')
A''_1 = Rotate(A', If[1  <  n  <  2, ((-(n - 2)) * α), 0], A'')
A''_2 = Rotate(A', If[1  <  n  <  2, ((-(n - 1)) * α), (-α)], A')
G'' = Rotate(G', If[1  <  n  <  2, ((-(n - 1)) * α), (-α)], A')
m' = Segment(A''_2, G'')
q = Circle(C', e)
H = Intersect(q, l, 1)
r = Segment(C', H)
s = Segment(F_1, G)
B' = Dilate(F_2, If[2  <  n  <  3, 3 - n, 1], D')
t = Vector(F_2, B')
G'_1 = Translate(G, t)
G'_2 = Translate(G, t)
B'_1 = Translate(F_2, t)
f' = Segment(G'_2, B'_1)
β = Angle(G, F_2, F_1)
a_1 = Segment(H, D')
b_1 = Segment(G, F_2)
A = Center(c)
A'_1 = Dilate(A, If[1  <  n  <  2, 2 - n, 0], C')
u_1 = Vector(F_1, A'_1)
A'_2 = Translate(A, u_1)
G'_3 = Translate(G, u_1)
e_1 = Segment(A'_2, G'_3)
γ = Angle(D, F_1, G)
B = Rotate(A'_2, ((-(n - 1)) * γ), A'_2)
I = Rotate(G'_3, ((-(n - 1)) * γ), A'_2)
G'_4 = Dilate(G, If[2  <  n  <  3, 3 - n, 0], D')
v_1 = Vector(G, G'_4)
A'_3 = Translate(A, v_1)
G'_5 = Translate(G, v_1)
g_1 = Segment(A'_3, G'_5)
J = Rotate(A'_3, If[2  <  n  <  3, ((-(n - 2)) * γ)], G'_4)
K = Rotate(G'_5, If[2  <  n  <  3, ((-(n - 2)) * γ)], G'_4)
k_1 = Circle(C', Distance[A''_2, G''])
i_1: y = y(C')
N = Intersect(k_1, i_1, 2)
j_1 = Segment(C', N)
O = Dilate(F_2, If[2  <  n  <  3, 3 - n], N)
w_1 = Vector(F_2, O)
G'_6 = Translate(G, w_1)
L = Translate(F_2, w_1)
f'_1 = Segment(G'_6, L)
p_1 = Circle(N, f)
M = Rotate(G'_6, If[2  <  n  <  3, ((n - 2) * β)], O)
L' = Rotate(L, If[2  <  n  <  3, ((n - 2) * β)], O)
l_1 = Segment(M, L')
m_1 = Segment(N, D')
C'' = Dilate(C', If[3  <  n ≤ 4, 4 - n], C)
D'' = Dilate(D', If[3  <  n ≤ 4, 4 - n], D)
n_1 = Segment(C'', D'')