# Question #a72c7

Sep 11, 2016

${r}^{2} \cos \left(2 \theta\right) = 9$

#### Explanation:

As there is no $z$ component, converting into cylindrical coordinates in this case is equivalent to converting to polar coordinates, which we can do using the identities

$\left\{\begin{matrix}x = r \cos \left(\theta\right) \\ y = r \sin \left(\theta\right)\end{matrix}\right.$

Substituting these in:

${x}^{2} - {y}^{2} = 9$

$\implies {\left(r \cos \left(\theta\right)\right)}^{2} - {\left(r \sin \left(\theta\right)\right)}^{2} = 9$

$\implies {r}^{2} \left({\cos}^{2} \left(\theta\right) - {\sin}^{2} \left(\theta\right)\right) = 9$

$\therefore {r}^{2} \cos \left(2 \theta\right) = 9$