How do you write the polar equations for 4x^2y=1?

Mar 18, 2017

$4 {r}^{3} {\cos}^{2} \theta \sin \theta = 1$

Explanation:

The relation between Cartesian coordinates $\left(x , y\right)$ and polar coordinates $\left(r , \theta\right)$ is given by

$x = r \cos \theta$ and $y = r \sin \theta$

Hence $4 {x}^{2} y = 1$ can be written as

$4 {r}^{2} {\cos}^{2} \theta \times r \sin \theta = 1$

or $4 {r}^{3} {\cos}^{2} \theta \sin \theta = 1$