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P(PF)

g = true
F = (5.92, 1.42)
F' = (-0.32, 1.56)
P = (5.56, 4.12)
b = Line(F', F)
O = Midpoint(F', F)
P' = Mirror(P, b)
P'_1 = Mirror(P, O)
P'' = Mirror(P', O)
c = Circle(P, F)
A' = Mirror(F', P)
a = Ray(P, A')
h = Segment(F', P)
Q_e = Intersect(c, a, 1)
Q_h = Mirror(Q_e, P)
f = Segment(P, Q_e)
i = Segment(P, F)
M_e = Midpoint(F', Q_e)
d = Circle(O, Segment[F', M_e])
A'_e, A_e = Intersect(d, b)
e = Conic(P, P'', P'_1, P', A_e)
M_h = Midpoint(F', Q_h)
k = Circle(O, Segment[F', M_h])
A'_h, A_h = Intersect(k, b)
p = Conic(P, P', P'_1, P'', A_h)

Tool: Conica DOsFocos Punto (command ConicaDOsFocosPunto)
Dar dos focos y un punto
Input: F_2, F_1, P
Output: e, p

O = Midpoint(F_2, F_1)
c = Circle(P, F_1)
A' = Mirror(F_2, P)
a = Ray(P, A')
E = Intersect(c, a, 1)
M_e = Midpoint(F_2, E)
d = Circle(O, Segment[F_2, M_e])
b = Line(F_2, F_1)
A'_e, A_e = Intersect(d, b)
E' = Mirror(E, P)
M_h = Midpoint(F_2, E')
k = Circle(O, Segment[F_2, M_h])
A'_h, A_h = Intersect(k, b)
P' = Mirror(P, b)
P'_1 = Mirror(P, O)
P'' = Mirror(P', O)
p = Conic(P, P', P'_1, P'', A_h)
e = Conic(P, P'', P'_1, P', A_e)