Question

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

Answer 1

Step-by-step explanation:

Given that,

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

The polar equation of the conic is given by :

$r=\dfrac{ed}{1-e\cos\theta}$

Put all the values,

$r=\dfrac{-5\times 2}{1-2\cos\theta}\\\\=\dfrac{-10}{1-2\cos\theta}$

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