Auxhiliary circle to hyperbola
Author: Daniela Velichová

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

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

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

Part of the circle can be created
by moving the point T along the hyperbola c.

F1 = (-1, -1)
F2 = (0.6351752609046653, 0.656466611651154)
c = Hyperbola(F1, F2, 0.8)
S = Midpoint(F1, F2)
a_1 = Line(F1, F2)
A, B = Intersect(c, a_1)
T = Point(c)
t, b = Tangent(T, c)
k_1 = OrthogonalLine(F1, t)
P_1 = Intersect(t, k_1)
k_2 = OrthogonalLine(F2, t)
P_2 = Intersect(k_2, t)
a = Segment(S, P_1)
d = Circle(S, A)