How do you write a formula for Hyperbolic circles, horocycles and hypercycles in Normal form give a point of rotation, or translation?
Specifically,
- a hyperbolic rotation (hyperbolic circle) about the point 1/2
- A parallel displacement (horocycle) about the ideal point -1
- A hyperbolic translation (hypercycle) from -i to i
I'm pretty confused.
I think Normal form is:
(Tz-p)/(Tz-q)=λ (z-p)/(z-q)
If the problem I am working didn't suggest using normal form I would think I could write the equation of a cycle, for the first two, with the center as the point of rotation.