# How do you convert r sec theta = 3 into cartesian form?

Sep 30, 2016

${x}^{2} + {y}^{2} = 3 x$

#### Explanation:

The relation between polar coordinates $\left(r , \theta\right)$ and Cartesian coordinates $\left(x , y\right)$ is given by

$x = r \cos \theta$, $y = r \sin \theta$ and ${r}^{2} = {x}^{2} + {y}^{2}$

Hence $r \sec \theta = 3$

$\Leftrightarrow r \times \frac{1}{\cos} \theta = 3$

or $r = 3 \cos \theta$

or ${r}^{2} = 3 r \cos \theta$

or ${x}^{2} + {y}^{2} = 3 x$
graph{x^2+y^2=3x [-3.867, 5.322, -2.057, 2.538]}