Answer
$r=\dfrac{12}{3-2 \cos \theta}$
and the conic is an ellipse as $0 \lt e \lt 1$
Work Step by Step
From the given statement , we have: Directrix , $a=6$ to the left of the pole and eccentricity ; $e=\dfrac{2}{3}$
The equation must be of the form as follows: $r=\dfrac{ae}{1-e \cos \theta}$
Then, we have $r=\dfrac{(6)(2/3)}{1-(2/3) \cos \theta}$
Therefore, $r=\dfrac{12}{3-2 \cos \theta}$
and the conic is an ellipse as $0 \lt e \lt 1$
