$t_1$

$t_2$

$O$

$c_p$

$F_1$

$F'_1$

$F_2$

$F'_2$

A = (-3.7714111279760862, -2.363846352939925)
B = (7.621604670837678, 5.619194879639547)
t_1 = Line(A, B)
C = (-2.343979914203596, 5.487025322808761)
D = (11.32235226209969, -1.3857916323921087)
t_2 = Line(C, D)
O = (3.013933581797437, -0.8580646082066196)
F = (6.775719507120647, -2.4431480870383964)
c_p = Circle(O, F)
E, H = Intersect(c_p, t_1)
G, I = Intersect(c_p, t_2)
a = OrthogonalLine(G, t_2)
b = OrthogonalLine(I, t_2)
c_1 = OrthogonalLine(E, t_1)
c = OrthogonalLine(H, t_1)
F_1 = Intersect(a, c_1)
F'_1 = Mirror(F_1, O)
F_2 = Intersect(a, c)
F'_2 = Mirror(F_2, O)
J = Mirror(F_1, t_1)
d = Line(J, F'_1)
K = Intersect(t_1, d)
L = Mirror(F_1, t_2)
e = Line(L, F'_1)
M = Intersect(e, t_2)
K' = Mirror(K, O)
M' = Mirror(M, O)
f = Line(F_1, O)
K'_1 = Mirror(K, f)
g = Conic(M, K, M', K'_1, K')
N = Mirror(F_2, t_1)
h = Line(N, F'_2)
P = Intersect(t_2, h)
Q = Mirror(F_2, t_2)
i = Line(Q, F'_2)
R = Intersect(t_1, i)
j = Line(F_2, F'_2)
Q' = Mirror(Q, O)
S = Intersect(i, t_2)
T = Intersect(t_1, h)
T' = Mirror(T, j)
T'_1 = Mirror(T, O)
S' = Mirror(S, O)
k = Conic(T', S, T, S', T'_1)