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Math Help - A small hyperbola question

  1. #1
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    A small hyperbola question

    a) if a comet travels along a hyperbola x^2/a^2 - y^2/b^2 = 1 and a planet locates at the focus (c,0), where c^2 = a^2 + b^2, find the closest distance that the comet ever comes to the planet. Give a sketch to illustrate the answer.

    b) if a=b=1, find that distance.
    Last edited by dull1234; January 11th 2009 at 08:18 PM. Reason: wrong spelling
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  2. #2
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    The closest point is (a,0). A point on the hyperbola can be represented as (a\cosh t, b\sinh t). The square of its distance from (\sqrt{a^2+b^2},0) is a^2\cosh^2t -a^2-b^2+b^2\sinh^2t. Use calculus to find that this has its minimum value at t=0.
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