# How do you convert r=100/(3-2costheta) into cartesian form?

Aug 17, 2016

$2491 {x}^{2} - 9 {y}^{2} - 10000 x + 10000 = 0$

#### Explanation:

The given polar equation is in the form

$\frac{a \left(1 - {e}^{2}\right)}{r} = 1 - s \cos \theta$ that represents an ellipse with

eccentricity $e = \frac{2}{3}$ ans semi major axis a = 60..

Use the conversion formula

$r \left(\cos \theta , \sin \theta\right) = \left(x , y\right)$ that gives

$r = \sqrt{{x}^{2} + {y}^{2}} \mathmr{and} \cos \theta = \frac{x}{r}$.

Substituting and rearranging,

$3 \left(\sqrt{{x}^{2} + {y}^{2}}\right) = 50 \left(2 - x\right)$. Squaring and rearranging,

,$2491 {x}^{2} - 9 {y}^{2} - 10000 x + 10000 = 0$