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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 $\lim_{e \to \infty}K = (2a, 0)$

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    I have some problems reading this. Doesn't $e\to\infty$ mean that conic section will sooner rather than later become a hyperbola? Yes, the curve can gradually transform into a hyperbola (and eventually, as a limit case, a straight line), but for the answer to make any sense this gradual transformation must take place in such a way that e.g. the scale won't suddenly blow up. In other words, there has to be a normalizing condition that you want to keep as a secret. Not cool :-( IOW give us the equation of the curve, where $e$ is a parameter.2011-07-19

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