$a$

$h$

$O$

$O(a)$

$A'$

$A$

$O(c)$

$F`$

$F$

A_1 = (-3.8, 5.74)
B = (8.2, 5.82)
a_1 = Ray(A_1, B)
C = Point(a_1)
a = Segment(A_1, C)
D = (-3.04, -0.9)
E = (5.7, 4.96)
h = Line(D, E)
F_1 = (-2.06, 1.58)
G = (6.02, 1.34)
b = Line(F_1, G)
O = Intersect(h, b)
c = Circle(O, a)
A', A = Intersect(c, b)
d = OrthogonalLine(A, b)
J = Intersect(h, d)
e = Circle(O, J)
F', F = Intersect(e, b)
f = Hyperbola(F, F', A)

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)