Ellipse Normal Length

Drag point T on the ellipse.  The length of the normal contained within the ellipse is then plotted as a locus against the x-coordinate of T in the 2nd Graphics Window. 
Drag points A, B and C to alter the shape and orientation of the ellipse

A = (2.777078372326132, 10.280178832741226)
B = (7.524949967248958, 2.9104592527579225)
C = (5.245221697711245, 9.857703849116747)
c = Ellipse(A, B, C)
T = Point(c)
a = Tangent(T, c)
b = OrthogonalLine(T, a)
E, F = Intersect(c, b)
d = Segment(T, F)
P: (x(T), d)
LengthLocus = Locus(P, T)
e = Segment(P, (x(P), 0))