Ellipse with Foci and Directices
Author: M. Dabbs, R. Walcott

Drag Point P.  Move point A

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 \frac{S_2P}{PD_2} = e

 \frac{S_1P}{PD_1} = e

Properties

S_1P + PS_2 = 2a

Properties

e = 0.631 (slider from 0.0010 to 1, step 0.01)
A = Point(xAxis)
A'_1 = Mirror(A, yAxis)
B = Intersect(xAxis, yAxis)
b = Dilate(A, e, B)
c = Circle(B, b)
l = true
m = false
a = Segment(B, A)
d = Circle(B, e * a)
f = Circle(B, a / e)
g = Circle(B, a * e)
S_1 = Intersect(g, xAxis, 1)
S_2 = Intersect(g, xAxis, 2)
h = Circle(B, a * sqrt(1 - e^(2)))
E = Intersect(h, yAxis, 1)
F = Intersect(h, yAxis, 2)
k = Ellipse(S_2, S_1, E)
G = Intersect(f, xAxis, 2)
H = Intersect(f, xAxis, 1)
i = OrthogonalLine(G, xAxis)
j = OrthogonalLine(H, xAxis)
P = Point(k)
n = Segment(S_1, P)
p = Segment(P, S_2)
q = Line(P, xAxis)
D_2 = Intersect(i, q)
D_1 = Intersect(j, q)
r = Segment(D_1, P)
s = Segment(P, D_2)