A complex number z is said to be uni modular if $|z|=1$ . Suppose $z_1$ and $z_2$ are complex numbers such that $ \large\frac{z_1 -2 z_2}{2-z_1z_2}$ is unimodular. Then the point $z_1$ lies on a :

Question

$\begin{array}{1 1} \text{straight line parallel to y-axis } \\ \text{circle of radius } \\ \text{circle of radius }\sqrt {2} \\ \text{straight line parallel to x-axis } \end{array} $