Consider a second coordinate system centered at $a$. The variable $z'$ will range over points in that system while $z$ will range over points in the original system. Then $z=z'+a$ (e.g.., the center $z'=0$ of the second system is mapped to $z=a$).
The equation of the required circle in the second system is $|z'|^2=a^2$. Express $z'$ through $z$ and substitute it into this equation. Then use the following properties.