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Thread: rectangular hyperbola question

  1. #1
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    Cool rectangular hyperbola question

    The point P(2p, 2/p) lies on the rectangular hyperbole xy=4
    The equation of the normal to H at P is y - 2/p = p2(x - 2p)
    The normal at P meets the hyperbola H again at the point Q. The midpoint of PQ is M.

    i) Find the coordinates of M

    ii) Find the cartesian equation of the locus of M as the position of P on H varies


    Mainly need some help with the second part. thanks!
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    Senior Member integral95's Avatar
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    Re: rectangular hyperbola question

    Hint: after you get M you then consider xy, then also consider x/y = -1\p^2 and y/x = -p^2
    “Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
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