A Mobius transformation maps circles to circles.
- Suppose I want a radius $r$ circle centered at point $(x,y)$ mapped to a radius $r'$ circle centered at $(x',y')$ what is the exact transformation?
A Mobius transformation maps lines to lines.
- Suppose I want a slope $m$ line through point $(x,y)$ mapped to a slope $m'$ line through $(x',y')$ what is the exact transformation?