$a$

$\vec{u}$

$h$

$P$

$O'$

$h'$

$A'_1$

$F'_2$

$F'_1$

$\Gamma$

$\delta$

recta de Pascal

$Q$

$\vec{v}$

$O$

$F_1$

$F_2$

$h''$

A = (-3.64, 5.5)
B = (9.18, 5.54)
a_1 = Ray(A, B)
C = Point(a_1)
a = Segment(A, C)
D = (-4.647286281500691, -4.861893309564326)
E = (-2.1163622612970348, -5.2921503929989475)
u = Vector(D, E)
F = (-0.1937560975609768, -1.180195121951224)
G = (9.09563114820516, 2.6296417902384936)
h = Line(F, G)
P = (9.247486589417377, -1.1414349998649531)
O' = Point(h)
H' = Translate(O', u)
v_1 = Vector(O', H')
b = Line(O', H')
h' = Mirror(h, b)
c = Circle(O', a)
I, A'_1 = Intersect(c, b)
d = OrthogonalLine(A'_1, b)
K = Intersect(h, d)
e = Circle(O', K)
F'_2, F'_1 = Intersect(e, b)
H'_1 = Mirror(O', h)
f = Hyperbola(F'_1, F'_2, A'_1)
g = Line(P, h)
i = Line(A'_1, h')
N = Intersect(g, i)
j = Line(O', N)
k = Line(A'_1, h)
O_1 = Intersect(j, k)
l = Line(O_1, h')
Q = Intersect(g, l)
v = Vector(Q, P)
O = Translate(O', v)
z = Vector(O', O)
F_1 = Translate(F'_1, v)
p = Vector(F'_1, F_1)
F_2 = Translate(F'_2, v)
q = Vector(F'_2, F_2)
s = Hyperbola(F_1, F_2, P)
h'' = Translate(h', v)

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)