Chapter 11: Parametric Equations and Polar Coordinates - Practice Exercises - Page 689: 82

$r=\dfrac{4}{1-\cos \theta}$

The polar equation of a conic with eccentricity $e$ and directrix $x=-k$ is written as: $r=\dfrac{ke}{1-e \cos \theta}$ Here, we have $e=1,k=4$ Thus $x=-k=-4$ Then $r=\dfrac{ke}{1-e \cos \theta}=\dfrac{4}{1-\cos \theta}$