Answer
$\dfrac{4}{1-\cos \theta}$
Work Step by Step
The polar equation of a conic with eccentricity $e$ and directrix $x=-k$ is:
$r=\dfrac{ke}{1-e \cos \theta}$ ...(1)
We are given that the vertices are: $e=1,k=4$
Then $x=-4$
Thus, equation (1), becomes
$r=\dfrac{4}{1-\cos \theta}$
