# Where is the vertical directrix of a conic if the denominator of its polar equation has the form 1-e cosq?

Feb 18, 2015

Hello !

You need the numerator.

If the polar equation of your conic is $r = \setminus \frac{p}{1 + e \setminus \cos \left(\setminus \theta\right)}$, both directrix are vertical and one of them contains the point $P \left(\setminus \frac{p}{e} , 0\right)$.

If the denominator is $1 - e \setminus \cos \left(\setminus \theta\right)$, write :

$1 - e \setminus \cos \left(\setminus \theta\right) = 1 + e \setminus \cos \left(\setminus \theta - \setminus \pi\right)$.

Both directrix are vertical and one of them contains the point $P \left(- \setminus \frac{p}{e} , 0\right)$.