## Precalculus (6th Edition) Blitzer

The rectangular equation is, $xy=1$
Using, $r\cos \theta =x$, and $r\sin \theta =y$ we will convert the polar equation to the rectangular equation. Therefore, \begin{align} & {{r}^{2}}\sin 2\theta =2 \\ & 2{{r}^{2}}\sin \theta \cos \theta =2 \\ & r\sin \theta \times r\cos \theta =1 \\ & xy=1 \end{align} Hence, the rectangular equation of ${{r}^{2}}\sin 2\theta =2$ is $xy=1$.