# Question #9cc39

Nov 18, 2017

${x}^{2} + {y}^{2} = \frac{6}{4} x + 7 y$

#### Explanation:

You will need to know these subsitutions:

${r}^{2} = {x}^{2} + {y}^{2}$
$\cos \left(\theta\right) = \frac{x}{r}$
$\sin \left(\theta\right) = \frac{y}{r}$

$r = \frac{6}{4} \cos \theta + 7 \sin \theta$

Substitute $\cos \theta$ and $\sin \theta$ with their appropriate substitutions.

$r = \frac{6}{4} \cdot \frac{x}{r} + 7 \cdot \frac{y}{r}$

Multiply both sides by $r$

${r}^{2} = \frac{6}{4} x + 7 y$

Substitute ${r}^{2}$ with it's appropriate substitution

${x}^{2} + {y}^{2} = \frac{6}{4} x + 7 y$

This is a valid rectangular equation.