# Replace the Cartesian equation with equivalent polar equations. xy = 2

Replace the Cartesian equation with equivalent polar equations. xy = 2
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tabuordg
$⇒\left(r\mathrm{cos}\theta \right)\left(r\mathrm{sin}\theta \right)=2$
${r}^{2}\mathrm{cos}\theta \mathrm{sin}\theta =2$
$⇒{r}^{2}\cdot \frac{\mathrm{sin}2\theta }{2}=2$
$⇒{r}^{2}\cdot \mathrm{sin}2\theta =4$
$⇒{r}^{2}=\frac{4}{\mathrm{sin}2\theta }$
$⇒{r}^{2}=4\mathrm{csc}2\theta$