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

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

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Nola Robson
$$\displaystyle\Rightarrow{\left({r}{\cos{\theta}}\right)}{\left({r}{\sin{\theta}}\right)}={2}$$
$$\displaystyle{r}^{{{2}}}{\cos{\theta}}{\sin{\theta}}={2}$$
$$\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\frac{{{\sin{{2}}}\theta}}{{{2}}}}={2}$$
$$\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\sin{{2}}}\theta={4}$$
$$\displaystyle\Rightarrow{r}^{{{2}}}={\frac{{{4}}}{{{\sin{{2}}}\theta}}}$$
$$\displaystyle\Rightarrow{r}^{{{2}}}={4}{\csc{{2}}}\theta$$