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Math Help - Parabola question

  1. #1
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    Parabola question

    Hi, I'll be grateful if you could help with this problem.

    The tangents of the parabola x2 - mx + 3/2 intersect perpendicularly at the origin, then what is the positive value of m?

    Thanks in advance.
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  2. #2
    MHF Contributor
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    Hi

    The equation of the tangent at the point whose abscissa is "a" is
    y = (2a-m)x-a+3/2

    The tangent passes through the origin when
    -a+3/2 = 0
    This gives 2 values : a1=sqrt(3/2) and a2=-sqrt(3/2)

    Spoiler:
    The two tangent intersect perpendicularly when
    (2a1-m)(2a2-m)=-1
    m-2(a1+a2)m+4a1a2=-1
    m-5=0
    m=+/-sqrt(5)
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  3. #3
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    Talking

    Thank you! You helped a lot!
    Last edited by truevein; June 6th 2010 at 02:00 PM.
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