# How do you convert 7 x+10 y = 0 to polar form?

Aug 28, 2016

$\theta + a r c \tan \left(0.7\right) = 0$.

#### Explanation:

To convert a cartesian eqn. into a polar, we need the following

conversion formulae $: x = r \cos \theta , y = r \sin \theta$, where, $r > 0$ and, $\theta \in \left(- \pi , \pi\right]$.

Sub. ing these in the given cartesian eqn., we get,

$7 \left(r \cos \theta\right) + 10 \left(r \sin \theta\right) = 0$

Since $r \ne 0 , \text{we have,} 10 \sin \theta = - 7 \cos \theta , \mathmr{and} , \tan \theta = - \frac{7}{10}$

$\therefore \theta = a r c \tan \left(- \frac{7}{10}\right) = - a r c \tan \left(0.7\right)$. Hence,

$\theta + a r c \tan \left(0.7\right) = 0$ is the reqd. polar eqn.