## Thomas' Calculus 13th Edition

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