Attachment 24734 Use the following ellipse : $\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (F, F' are foci of the ellipse and the line passes through it.)

Prove : $\displaystyle \frac{1}{PF}+\frac{1}{QF} = \frac{2a}{b^2}$

I tried to prove it using directrix, but it got way too complicated.