Given

$$x=r\,\cos\theta\\y=r\,\sin\theta$$ and
$$x'=r'\,\cos\theta'\\y'=r'\,\sin\theta'$$

how can I express

$$\delta(x'-x)\delta(y'-y)$$ in terms of the polar coordinates?

And the more general case:

$$\delta(x'-x-a)\delta(y'-y-b)$$