Question

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

Answer 1

Eccentricity is `2`, Focus is at the pole `(0,pi/2)`,
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 `(0,pi/2)` [Ans]