Tangent Not On Ellipse
Author: M. Dabbs, R. Walcott

Drag the point P.  Move the points A, S1 and S2

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Point of Tangency (1)

Point of Tangency (2)

S_1 = Point(a)
S_2 = Point(a)
O = Midpoint(S_1, S_2)
A = Point(a)
c = Circle(O, A)
d = Circle(O, S_2)
G = Point(c)
b = Line(S_1, G)
S'_1 = Dilate(S_1, -1.0, G)
e = Line(S_2, S'_1)
f = OrthogonalLine(G, b)
P_1 = Intersect(e, f)
loc1 = Locus(P_1, G)
P = (11.15213454241969, 4.2756662125683755)
g = Segment(P, S_2)
C = Midpoint(P, S_2)
h = Circle(C, P)
D, E = Intersect(c, h)
i = Line(P, D)
j = Line(P, E)
k = OrthogonalLine(S_1, i)
l = OrthogonalLine(S_1, j)
B = Intersect(i, k)
F = Intersect(l, j)
H = Mirror(S_1, i)
I = Mirror(S_1, j)
m = Line(S_2, I)
n = Line(S_2, H)
J = Intersect(i, n)
K = Intersect(j, m)
o = false
p = false