# Question 1eeff

Dec 16, 2017

The polar equation of parabola is $r = \frac{20}{1 + \sin \theta}$

#### Explanation:

The polar equation is r= (ed)/(1+esin (theta)# where

$e = 1$ ,the eccentricity of parabola and $d$ is directrix.

So the polar equation of parabola is $r = \frac{d}{1 + \sin \theta}$

The focus is at origin and vertex is at distance of $10$ unit

on positive $y$ axis at an angle of $\frac{\pi}{2}$. vertex is at equidistance

from focus and directrix. So directrix is $y = 20 \therefore d = 20$

Hence the polar equation of parabola is $r = \frac{20}{1 + \sin \theta}$

[Ans]