Answer
$r=\dfrac{20}{5+4\cos \theta}$
and the conic is an ellipse as $0 \lt e \lt 1$
Work Step by Step
From the given statement , we have: Directrix , $a=5$ to the right of the pole and eccentricity ; $e=\dfrac{4}{5}$
The equation must be of the form as follows: $r=\dfrac{ae}{1+e \cos \theta}$
Then, we have $r=\dfrac{(5)(4/5)}{1+(4/5) \cos \theta}$
Therefore, $r=\dfrac{20}{5+4\cos \theta}$
and the conic is an ellipse as $0 \lt e \lt 1$
