eje focal

O(a)

O(c)

O(a)

O(c)

A = (-30.28737009253954, -14.341664421571224)
B = (22.873116156451548, 20.183868180445256)
h_1 = Line(A, B)
C = (-31.326234362591055, 24.295784135939105)
D = (19.707972903689768, -12.905813292744826)
h_2 = Line(C, D)
O = Intersect(h_1, h_2)
P = (19.31839880242045, 9.284613243663133)
a = Line(P, h_1)
H_1 = Intersect(a, h_2)
b = Line(P, h_2)
H_2 = Intersect(h_1, b)
c = AngularBisector(H_2, O, H_1)
d = Line(P, c)
Q_1 = Intersect(d, h_1)
Q_2 = Intersect(h_2, d)
e = Semicircle(P, Q_1)
f = OrthogonalLine(Q_2, c)
M_1 = Intersect(e, f)
g = Semicircle(P, Q_2)
h = OrthogonalLine(Q_1, c)
M_2 = Intersect(g, h)
k = Circle(O, Segment[P, M_1])
E, F = Intersect(k, c)
i = OrthogonalLine(F, c)
G = Intersect(h_1, i)
p = Circle(O, G)
H, I = Intersect(p, c)
q = Hyperbola(I, H, P)
r = Circle(O, Segment[P, M_2])
J, K = Intersect(r, c)
j = OrthogonalLine(J, c)
L = Intersect(j, h_2)
s = Circle(O, L)
M, N = Intersect(s, c)
t = Hyperbola(M, N, P)

Tool: Hiperbola Punto Dos Asintotas (command HiperbolaPuntoDosAsintotas)
Dar un punto y las dos asíntotas
Input: P, h_1, h_2
Output: p, P', P'_1, P_1, P_2

E = Intersect(h_1, h_2)
P' = Mirror(P, E)
b = Line(P, h_2)
c = Line(P', h_1)
d = Line(P, h_1)
e = Line(P', h_2)
F = Intersect(e, d)
G = Midpoint(P', F)
f = Line(P, G)
H = Intersect(b, c)
g = Line(H, G)
h = Line(P', g)
P_1 = Intersect(f, h)
P'_1 = Mirror(P_1, E)
J = Midpoint(G, F)
i = Line(P, J)
j = Line(H, i)
K = Intersect(h_2, j)
k = Line(K, P')
P_2 = Intersect(i, k)
p = Conic(P', P_1, P_2, P, P'_1)