Polar Equation and Conic

Question

Find a polar equation of the conic with focus at the pole, eccentricity of 1/3, and a directrix with the equation of r=5sec(theta).

Answer 1

For directrix we have r = 5secθ; rcosθ = 5; x = 5.

So, polar equation of conic: r = ed/(1 + ecosθ);

we have d = 5; e = 1/3.

So, polar equation: r = 5/3/(1 + 1/3cosθ) or r = 5/(3 + cosθ)