Answer
$r=\dfrac{2}{2+\sin \theta}$
Work Step by Step
The polar equation of a conic with eccentricity $e$ and directrix $y=k$ is written as:
$r=\dfrac{ke}{1+e \sin \theta}$
Here, we have $e=\dfrac{1}{2},k=2$
Thus $y=k=2$
Then
$r=\dfrac{ke}{1+e \sin \theta}=\dfrac{1}{1+(\dfrac{1}{2})\sin \theta}$
or, $r=\dfrac{2}{2+\sin \theta}$
