1. ## Conics question

A straight line D through the focus F of a conic $\Phi$ meets $\Phi$ in two points A and B.
Show that the quantity
$\frac{1}{|AF|} + \frac{1}{|BF|}$
is independent of the choice of line D.
Not sure where to start with this one apart from maybe trying the 3 different conics of hyperbola, parabola and ellipse. Could someone give me a hint where to start?

2. All conics can be expressed in polar form as:
$r(\theta) = \frac{l}{1 - e cos(\theta)}$, where the focus is at the origin.
A line that passes through the focus would intersect at points $r(\theta_0)$ and $r(\theta_0 + \pi)$

so $\frac{1}{|AF|} + \frac{1}{|BF|} = \frac{1}{r(\theta_0)} + \frac{1}{r(\theta_0 + \pi)}$

Can you show that this does not depend on $\theta_0$?