$a$

$b$

$O$

$O(a)$

$A$

$A'$

$b$

$M$

$O(OM)$

$F'$

$F$

$X$

$F(AX)$

$F'(A'X)$

$P'$

$P$

A_1 = (-2.663733390237294, 5.367352456497295)
B = (10.14, 5.28)
a_1 = Ray(A_1, B)
a = Point(a_1)
c = Segment(A_1, a)
b = Point(a_1)
d = Segment(A_1, b)
O = (4.64, -0.14)
e = Circle(O, Segment[A_1, a])
A = Point(e)
A' = Mirror(A, O)
f = Line(A', A)
g = OrthogonalLine(A, f)
h = Circle(A, Segment[A_1, b])
C = Intersect(h, g, 2)
i = Segment(A, C)
M: C
k = Circle(O, M)
F', F = Intersect(k, f)
O' = Mirror(O, F)
j = Ray(F, O')
X = Point(j)
p = Circle(F, Segment[X, A])
q = Circle(F', Segment[A', X])
P', P = Intersect(p, q)
r = Hyperbola(F, F', P)
l = Line(O, M)
l' = Mirror(l, f)