Cónica de la que se conoce su eje e_1, un foco F 
y dos puntos P_1 y P_2 alineados con F

\mathcal C

F'

M

A = (2.3037882429417817, -0.10425638987309616)
B = (24.93858842647883, 0.0727755668696501)
e_1 = Line(A, B)
F = Point(e_1)
C = (20.398855534092462, 7.012527661983881)
d = Line(F, C)
P_1 = Point(d)
P_2 = Point(d)
D = Midpoint(P_1, P_2)
P1P2 = Circle(D, P_1)
cod = IsInRegion(F, P1P2)
E = Midpoint(D, P_1)
d_1 = Circle(P_1, Segment[F, E])
F_d = Mirror(F, D)
e = Circle(P_2, Segment[F_d, E])
G, H = Intersect(d_1, e)
G' = Mirror(G, D)
H' = Mirror(H, D)
f = Conic(F, G, H, G', H')
F' = SegundoPuntoRectaConica(F, G, H, G', H', e_1)
M = Midpoint(F, F')
I = Mirror(P_1, e_1)
J = Mirror(P_2, e_1)
K = Mirror(P_1, M)
g = Conic(P_1, P_2, I, J, K)
F'_1 = Mirror(F, P_1)
c = Circle(P_1, Segment[F, F'_1])
h = Circle(P_2, Segment[F_d, F'_1])
L, N = Intersect(h, c)
L' = Mirror(L, D)
N' = Mirror(N, D)
k = Conic(F, L, N, L', N')
O = SegundoPuntoRectaConica(F, L, N, L', N', e_1)
P = Midpoint(F, O)
Q = Mirror(P_1, P)
p = Conic(P_1, I, P_2, J, Q)

Tool: Segundo Punto Recta Conica (command SegundoPuntoRectaConica)
Dar ABCDE y recta por A
Input: A0, B0, C0, D0, E0, b
Output: A'

e = Line(A0, C0)
f = Line(B0, E0)
P0 = Intersect(e, f)
g = Line(B0, D0)
Q0 = Intersect(b, g)
h = Line(C0, D0)
i = Line(P0, Q0)
R0 = Intersect(h, i)
j = Line(E0, R0)
A' = Intersect(b, j)