# How do you convert x^2 = 6y into polar form?

Apr 15, 2018

Polar form is $r = \tan \theta \cdot \sec \theta$

#### Explanation:

${x}^{2} = 6 y$. The relation between polar and Cartesian coordinates

are ${r}^{2} = {x}^{2} + {y}^{2} , \tan \theta = \frac{y}{x} , x = r \cos \theta , y = r \sin \theta$

${x}^{2} = 6 y \therefore {\left(r \cos \theta\right)}^{2} = r \sin \theta$ or

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

$r = \sin \frac{\theta}{\cos} ^ 2 \theta \mathmr{and} r = \tan \theta \cdot \sec \theta$

Polar form is $r = \tan \theta \cdot \sec \theta$

[Ans]