# How do you convert r=8cos(theta) into cartesian form?

Jul 13, 2016

${x}^{2} + {y}^{2} = 8 x$

#### Explanation:

As relation between Cartesian coordinates $\left(x , y\right)$ and polar coordinates $\left(r , \theta\right)$ is given by $x = r \cos \theta$ and $y = r \sin \theta$ i.e. ${r}^{2} = {x}^{2} + {y}^{2}$.

As $r = 8 \cos \theta$ can be written as

r×r=8rcostheta or

${r}^{2} = 8 r \cos \theta$ or

${x}^{2} + {y}^{2} = 8 x$

Note - This is the equation of a circle with center at $\left(4 , 0\right)$ and radius $4$.