circle catacaustic

This equation describes the circle catacaustic, the (cata)caustic of a circle, given a circle
with radius =1, and a light source placed at (a, 0).
Some authors state that this curve is the limaçon (but this is not true).

Two special situations are the following:

• a = 1 (light source on circle): cardioid
• a = ∞ (parallel rays): nephroid