Answer
$\dfrac{2}{4-\cos \theta}$
Work Step by Step
The polar equation of a conic with eccentricity $e$ and directrix $x=-k$ is defined as:
$r=\dfrac{ke}{1-e \cos \theta}$ ...(1)
We are given that the vertices are: $e=\dfrac{1}{4},k=2$
Then $x=-2$
Thus, equation (1), becomes
$r=\dfrac{(\dfrac{1}{2})}{1-(\dfrac{1}{4})\cos \theta}=\dfrac{2}{4-\cos \theta}$
