# How do you convert xy=16 to polar form?

Apr 11, 2016

${r}^{2} \sin 2 \theta = 32$

#### Explanation:

Relation between polar coordinates $\left(r , \theta\right)$ and rectangular coordinates $\left(x , y\right)$ is given by $x = r \cos \theta$ and $y = r \sin \theta$.

Hence $x y = 16$ is equivalent to

${r}^{2} \sin \theta \cos \theta = 16$ or

${r}^{2} \times 2 \sin \theta \cos \theta = 32$ or

${r}^{2} \sin 2 \theta = 32$

graph{xy-16=0 [-10, 10, -10, 10]}