Polar Represantation of Shifted Disk

Question

How to represent a shifted circle or disk (I mean the center of the circle is not at origin) in polar coordinate?

For example I have a circle/disk in z-Domain like this:

I thought this:

$z = re^{j\theta}$;

subject to:

$0 < r < 2$ and $-\pi/2<\theta<\pi/2$

But I think it isn' t right.

Answer 1

Suppose the centre of the circle is $r_oe^{i\theta_o}$. If we want a circle of radius $c$, it is given by $2-2rr_ocos(\theta-\theta_o)=c^2$.