Constructed Hyperbola and Ellipse
Author: Farrar

Drag point A to see the corresponding point P on the locus.

Movable points:  the two focus points f_1 and f_2, along with the point resizecircle.  Observe how each changes the locus.

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f_1 = (2, 2)
f_2 = (6, 2)
a_1 = Segment(f_1, f_2)
center = Midpoint(a_1)
resizecircle = (-3.2089697686620857, 3.0439288090349383)
c_1 = Circle(f_1, resizecircle)
A = Point(c_1)
b_1 = Segment(f_2, A)
d = Line(f_1, A)
e = LineBisector(b_1)
P = Intersect(d, e)
loc1 = Locus(P, A)
d_1 = Segment(f_1, P)
d_2 = Segment(f_2, P)
c = Segment(center, f_2)
α = Angle(b_1, e)
f = Circle(center, f_1)
r_0 = Distance(f_1, resizecircle)
Textf1resizecircle: "\overline{" + (Name[f_1]) + (Name[resizecircle]) + "} \, = \, " + r_0
g = Circle(center, r_0 / 2)
h = Line(f_1, f_2)
v_1, v_2 = Intersect(g, h)
a = Segment(v_1, center)
i = OrthogonalLine(v_1, a)
B = Intersect(f, i, 2)
b = Segment(v_1, B)
j = false
k = false
p = Circle(f_1, a)
l = OrthogonalLine(center, h)
C, D = Intersect(p, l)
b_e = Segment(center, D)
c' = Segment(B, center)
a' = Segment(D, f_1)
m: d_1 + d_2
text1: "d_1+d_2 =" + m
n: abs(d_2 - d_1)
text2: "| d_2 - d_1 | =" + n
text3: "eccentricity = " + (c / a)