Is there a radially symmetric density over the unit disk in the form of

f(x^2+y^2)

such that the marginal

$\displaystyle \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} f(x^{2}+y^{2})dy=c

$

I don't know how to start finding this function... Tried using calculus of variations but couldn't make it work.