Given the following polar equation
![\[ r = \frac{4}{1+ \cos \theta} \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-ffae26c81f6eaa16dc7dd0f8c373e350_l3.png "Rendered by QuickLaTeX.com")
for a conic section with a focus 
at the origin and vertical directrix lying to the right of , determine the eccentricity 
and the distance 
from the focus to the directrix.
By Theorem 13.18 we know the points on a conic section satisfy the polar equation
![\[ r = \frac{ed}{1 + e \cos \theta}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-dbff264e45f1e7d239bd0749f577f580_l3.png "Rendered by QuickLaTeX.com")
Therefore, 
and 
, so 
.