# How do you write the polar equations for y^2=2x?

Dec 3, 2015

${r}^{2} {\sin}^{2} \left(\theta\right) = 2 r \cos \left(\theta\right)$

#### Explanation:

In polar coordinates, the coordinates are

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

So,

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

If $r \setminus \ne 0$ (which means $\left(x , y\right) \setminus \ne \left(0 , 0\right)$, we can simplify one $r$ and have

$r {\sin}^{2} \left(\theta\right) = 2 \cos \left(\theta\right)$