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

EunoR

## Answered question

2021-11-06

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

### Answer & Explanation

$\Rightarrow \left(r\mathrm{cos}\theta \right)\left(r\mathrm{sin}\theta \right)=2$

${r}^{2}\mathrm{cos}\theta \mathrm{sin}\theta =2$

$\Rightarrow {r}^{2}\cdot \frac{\mathrm{sin}2\theta}{2}=2$

$\Rightarrow {r}^{2}\cdot \mathrm{sin}2\theta =4$

$\Rightarrow {r}^{2}=\frac{4}{\mathrm{sin}2\theta}$

$\Rightarrow {r}^{2}=4\mathrm{csc}2\theta$

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