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Math Help - Conics - Locus Question

  1. #1
    GaDaMIt
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    Conics - Locus Question

    Hey, im new here, got a quick conics question. Im not sure if it really belongs here but it still is high school maths. Anyway..

    The line y = mx + c is a tangent to the hyperbola x^2/25 - y^2/16 = 1. Show that c^2 = 25m^2 - 16. Done this bit
    The tangents from P(x1, y1) to this hyperbola meet at right angles. Prove that the locus of P is the circle x^2 + y^2 = 9
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by GaDaMIt View Post
    ...
    The line y = mx + c is a tangent to the hyperbola x^2/25 - y^2/16 = 1. Show that c^2 = 25m^2 - 16. Done this bit
    The tangents from P(x1, y1) to this hyperbola meet at right angles. Prove that the locus of P is the circle x^2 + y^2 = 9
    Hello,

    unfortunately I cann't offer you a (algebraic) solution. But I've done a rather exact construction (with a little help from my PC of course). I send you an image to show you that the statement is true. And maybe it helps to find a way to do the problem.

    EB
    Attached Thumbnails Attached Thumbnails Conics - Locus Question-hyp_gemnsamtangent.gif  
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