I need proof for the following question. Also, I want to know, can we apply the same for other conics. If yes, where and when... Please explain.
Show that there exists a point K on the major axis of E , having the property that for any chord $\overline{PQ}$ passing through K, $\dfrac{1}{PK^2} + \dfrac{1}{QK^2}$ is a constant. Also Show that $\lim_{e \to \infty}K = (2a, 0)$