Answer
$(x^2+y^2)^2=8xy$.
Work Step by Step
To convert from polar to rectangular coordinates we use $x=r\cos\theta$ and $y=r\sin\theta$. To convert from rectangular to polar coordinates, we use $r=\pm\sqrt{x^2+y^2}$, $\tan\theta=\frac{y}{x}$, but aware of which quadrant the point lies in.
Hence here $r^2=4\sin2\theta=8\cos\theta\sin\theta\\r^4=8r\cos\theta r\sin\theta \\(x^2+y^2)^2=8xy$.
