Joint Density function Question

Hi all,

I have been going though a Q and have no idea how to even start it:

Q:

Suppose that have the joint distribution:

,

Find c..?

Now my initial thoughts are that the bounded unit cirrcle region gives the limits of integration such that:

, in our case A is bound by the unit circle, giving:

does this look like the right method to employ? I am not convinced..... the answer in the text book (no method though) ... can anyone offer any guidance on this one??

Many thanks for reading!