JEE Math Practice Question

If $$z_1, z_2$$ are two distinct complex number such that $$\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2$$, then

1. A.either $$z_1$$ lies on a circle of radius $$\frac{1}{2}$$ or $$z_2$$ lies on a circle of radius 1.
2. B.$$z_1$$ lies on a circle of radius $$\frac{1}{2}$$ and $$z_2$$ lies on a circle of radius 1.
3. C.either $$z_1$$ lies on a circle of radius 1 or $$z_2$$ lies on a circle of radius $$\frac{1}{2}$$.
4. D.both $$z_1$$ and $$z_2$$ lie on the same circle.