Answer
$r=\dfrac{6}{3-\sin \theta}$
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 $e=\dfrac{1}{3},k=6$
Then $y=-k=-6$
Then, $r=\dfrac{ke}{1- e \sin \theta}=\dfrac{2}{1-(\dfrac{1}{3})\sin \theta}$
or, $r=\dfrac{6}{3-\sin \theta}$
