## Thomas' Calculus 13th Edition

$r=\dfrac{8}{1+2\cos \theta}$
The equation of conic with eccentricity $e$ and directrix $x=k$ leads to focus can be written as: $r=\dfrac{ke}{1+e \cos \theta}$ ....(1) Given: $e=2,k=4$ Then $x=4$ Thus, the equation (1) can be written as: $r=\dfrac{ke}{1+e \cos \theta}=\dfrac{8}{1+2\cos \theta}$