Calculus (3rd Edition)

The conic section is an ellipse with $e=3/4$ and directrix $x=4$.
Converting the given equation to the standard form $$r=\frac{e d}{1+e \cos \theta}.$$ We get $$r=\frac{12}{4+ 3\cos \theta}=\frac{3}{1+(3/4) \cos \theta}.$$ Then we have $ed=3, e=\frac{3}{4} .$ Thus, $d=4$ and the directrix equation is $x=4$. Since $e\lt 1$, then the conic section is an ellipse.