Problem

Experiment

Construction

Locus 1

Solution

Proof

Locus 2

γ = 0.5061454830783556 rad (slider from -89° to 90°, step °)
J = (-1.3682212114980643, 5.343403072702768)
B = Point(xAxis)
A = Point(xAxis)
a = Segment(A, B)
r = Line(J, a)
C = Point(r)
b = OrthogonalLine(C, a)
f = false
e = LineBisector(a)
E = Point(e)
g = Circle(E, B)
F = Point(g)
h = Segment(A, F)
i = Segment(F, B)
β = Angle(A, F, B)
j = false
k = OrthogonalLine(C, e)
n = false
o = false
K = Intersect(e, a)
v = false
D = Point(b)
D' = Rotate(D, γ, C)
α = Angle(D, C, D')
s = Line(C, D')
c = Parabola(B, s)
G = Intersect(c, e, 2)
d = Circle(G, B)
H = Intersect(d, s, 1)
loc1 = Locus(H, C)
O = (0, 0)
t = Rotate(xAxis, γ / 2)
I = Point(loc1)
L = Point(loc1)
M = Point(loc1)
p = Conic(I, A, B, L, M)
N = Intersect(p, t, 1)
l = OrthogonalLine(O, t)
m = false
P = Point(s)
q = Segment(P, A)
a_1 = Segment(P, B)
δ = Angle(A, P, B)
loc2 = Locus(N, γ)
N' = Intersect(p, t, 2)