I have some difficulty with converting this implicit, Cartesian function into polar form: $\left(y^2+x^2\right)^2=2\left(x^2-y^2\right)$
I know that, in order to attempt to convert it, I need to use $x=r\cos\left(\theta\right)$ and $y=r\sin\left(\theta\right)$ and $x^2+y^2=r ^2;$ however, when I try applying these substitutions it seems like the $r$ cancels out and I'm left with a function independent of $r$.
Am I missing anything important? Thank you for the answers in advance!
$$\rho^4=2\rho^2\cos2\theta$$
is also
$$\rho=\sqrt{2\cos2\theta},$$
which is a lemniscate.