#### Answer

$3$, $hyperbola$, $1$, $perpendicular$, $1$, $right$.

#### Work Step by Step

Comparing the given equation $r=\frac{3}{1+3cos\theta}$ with the standard forms (a), we can identify that $e=3$, so this is the equation of a $hyperbola$. We see that $ep=3, p=1$, so the directrix is $perpendicular$ to the polar axis at a distance of $1$ unit to the $right$ of the pole.