Question

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

Answer 1

Hello !

You need the numerator.

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

If the denominator is `1-e\cos(\theta)`, write :

`1-e\cos(\theta) = 1 + e\cos(\theta - \pi)`.

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