How do you find the eccentricity, directrix, focus and classify the conic section r=2/(1+2costheta)?

Jun 16, 2018

Eccentricity is $2$, Focus is at the pole $\left(0 , \frac{\pi}{2}\right)$,
Directrix is $p = 1$ unit at right from the pole.
Conic: Hyperbola

Explanation:

r= 2/(1+2 cos theta .The equation is in the form

r= (ep) /(1+e cos theta) ; e =2 since $e > 1$ the conic

is hyperbola. r= (ep) /(1+e cos theta) ; e p =2 :. p=1

Directrix is at $p = 1$ unit at right from the pole.

Eccentricity is $2$ , Focus is at the pole $\left(0 , \frac{\pi}{2}\right)$ [Ans]