Auxhiliary circle to ellipse
Author: Daniela Velichová

Auxhiliary circle to an ellipse is the set of all points that are 
intersections of all ellipse tangent lines and perpendiculars 
passing through both ellipse foci to these tangent lines.

Centre of the auxhiliary circle is in the ellipse centre S,
its radius equals to the ellipse semi-major axis a.

Auxhiliary circle is passing through 
the ellipse major vertices A and B. 

Auxhiliary circle can be generated 
by moving the tangent point T along the ellipse c.

F1 = (-1, -1)
F2 = (0.6351752609046653, 0.656466611651154)
c = Ellipse(F1, F2, 1.7)
S = Midpoint(F1, F2)
T = Point(c)
t, b = Tangent(T, c)
k_1 = OrthogonalLine(F1, t)
P_1 = Intersect(k_1, t)
k_2 = OrthogonalLine(F2, t)
P_2 = Intersect(t, k_2)
a = Segment(P_1, S)
d = Circle(S, P_2)
A = Intersect(c, d, 3.0)
B = Intersect(c, d, 1.0)
e = Segment(A, B)