Answer
$r= \dfrac{9}{1 + 3 \cos(θ)}$
Work Step by Step
The polar equation of a conic with eccentricity $e$ and a vertical line directrix is:
$r= \dfrac{ed}{1 + e \cos (θ)}$
Given; $e = 3$ and directrix is at x=3.
Now, we have $r= \dfrac{ed}{1 + e \cos (θ)}=\dfrac{(3) (3)}{1 + (3) \cos(θ)}$
Hence, $r= \dfrac{9}{1 + 3 \cos(θ)}$
