Question

Find the polar equation of the conic with the focus at the pole, directrix x = -5, and eccentricity 2.

Answer 1

Explanation:

Given that,

Directrix, d= -5, and eccentricity, e = 2.

The polar equation of the conic is given by :

`r=(ed)/(1-e\cos\theta)`

Put all the values,

`r=(-5* 2)/(1-2\cos\theta)\\\\=(-10)/(1-2\cos\theta)`

As e>1, it is a hyperbola. Hence, this is the required solution.