$a$

$F_1$

$F_2$

$F_2(2a)$

$M$

$P$

A = (-3.72, 5.4)
B = (9.76, 5.44)
a_1 = Ray(A, B)
C = Point(a_1)
a = Segment(A, C)
F_1 = (5.7, 1.04)
F_2 = (1.46, 0.92)
c = Circle(F_2, 2 * a)
M = Point(c)
b = LineBisector(M, F_1)
d = Line(M, F_2)
P = Intersect(b, d)
e = Hyperbola(F_1, F_2, P)
f = Circle(F_1, 2 * a)
g = Circle(M, Segment[F_2, F_1])
E, F = Intersect(f, g)
lugar1 = Locus(E, M)
h = Line(F_1, E)
i = Line(F_1, F)