(D)

e = 0.6 (slider from 0 to 5, step 0.1)
c: x^(2) + y^(2) = (e^(2) * (x + 1)^(2))
P = Point(c)
F = Intersect(yAxis, xAxis)
f = Line(P, F)
h = OrthogonalLine(F, f)
T = Intersect(d, h)
i = Line(T, P)
U = Intersect(i, a)
b = OrthogonalLine(P, i)
V = Intersect(b, a)
f' = Mirror(f, b)
H = Intersect(d, a)
A = Dilate(H, e / (e + 1), F)
A' = Dilate(H, e / (e - 1), F)
O = Midpoint(A, A')
F' = Mirror(F, O)
g = OrthogonalLine(V, b)
Q = Intersect(f, g)
j = OrthogonalLine(Q, f)
C = Intersect(b, j)
k = Circle(C, P)
l = Segment(Q, C)
m = Segment(Q, V)
n = Segment(P, F')
F'' = Mirror(F', b)
p = OrthogonalLine(F'', f)
J = Intersect(b, p)
q = OrthogonalLine(F, f)
I = Intersect(q, b)
r = Segment(F'', J)
s = Segment(F, I)
t = Circle(P, F', F'')
F'_1 = Mirror(F, b)
c_1 = Circle(P, F, F'_1)