> 
> Suppose $|a|<1$ and $r\in (0,1)$. Show that the set of complex number $z$ satisfying $\left|\dfrac{z-a}{1-\bar a z}\right|=r$ is a circle in complex plane. Find the centre and radius of this circle.
> 
> 
> 

By putting $z=x+iy$ and $a=a\_1+ia\_2$ and then simplifying I got the result, but the process is too lengthy. I want a short and tricky way that the equation represents a circle.