Hyperbolic Line

Select two points to create a hyperbolic line through them

Hyperbolic Ray

Select two points to create a hyperbolic ray through them.

(y * y(B)) = (-((x(B))^(2) + (y(B))^(2) + (x(B) * x) + 1))
(y * y(A)) = (-((x(A))^(2) + (y(A))^(2) + (x(A) * x) + 1))
C = Intersect(a, b)
d: x(C)
e: y(C)
D: (((-d)) / 2, ((-e)) / 2)
f = Circle(D, A)
E = Point({Intersect[x^(2) + y^(2) = 1, f]}, If[Angle[B, D, A] < 180°, 1, 0])
F = Point({Intersect[x^(2) + y^(2) = 1, f]}, If[Angle[B, D, A] < 180°, 0, 1])
g = Ray(B, A)
h = Ray(A, B)
G, N = Intersect(x^(2) + y^(2) = 1, g)
H, O = Intersect(x^(2) + y^(2) = 1, h)
I = If(Defined[D], E, G)
J = If(Defined[D], F, H)
K = Midpoint(A, B)
i = Ray(D, K)
L = Intersect(f, i, 1)
M = If(Defined[L], L, K)
k = CircumcircleArc(I, M, J)
d, C, D = HyperbolicLine(A, B)
e = CircumcircleArc(A, B, C)
f = CircumcircleArc(A, B, D)
g = If(e < f, e, f)
E = If(e < f, C, D)