A straight line D through the focus F of a conic $\displaystyle \Phi$ meets $\displaystyle \Phi$ in two points A and B.

Show that the quantity

$\displaystyle \frac{1}{|AF|} + \frac{1}{|BF|}$

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?