How do I find all linear fractional transformations which map the circle $\{z\in \Bbb{C}:|z-2|=3\}$ to itself?

Question

I have the following problem.

I need to find all linear fractional transformations $f$ such that $f(\{|z-2|=3\})=\{|z-2|=3\}$

I thought that maybe one could use that a LFT maps symmetric points with respect to $\{|z-2|=3\}$ to symmetric points with respect to $\{|z-2|=3\}$. But I'm a bit confused since I need to find all of them not only one. Could someone give me a hint?

Thanks for your help.