Answer
$\dfrac{1}{2+\cos \theta}$
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: $e=\dfrac{1}{2},k=1$
Then $x=1$
Thus, equation (1), becomes
$r=\dfrac{(\dfrac{1}{2})}{1+(\dfrac{1}{2})\cos \theta}=\dfrac{1}{2+\cos \theta}$
