Answer
$\dfrac{10}{5-\cos \theta}$
Work Step by Step
The polar equation of a conic with eccentricity $e$ and directrix $y=-k$ is defined as:
$r=\dfrac{ke}{1-e \sin \theta}$ ...(1)
We are given that the vertices are: $e=\dfrac{1}{5}$
Thus, equation (1), becomes
$r=\dfrac{2}{1-(\dfrac{1}{5})\sin \theta}=\dfrac{10}{5-\cos \theta}$
