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Cubic and Ellipse problem

  1. Nov 2, 2007 #1
    The question im looking at states:
    Prove that the elliptical function x^2 + 3y^2=b is orthogonal to the cubic y=3ax^3.

    I'm thinking they want me to prove if the functions are orthogonal when they intersect. If im correct that would just lead to;

    For the ellipse,
    2x+6y(m1)=0, m1=-x/3y, when they intersect: m1=-x/3(3ax^3)=-1/9ax^2

    Cubic,
    m2=9ax^2

    m1xm2=[-1/9ax^2][9ax^2]=-1, Therefore they are orthogonal when they intersect.

    Am I right here? Is this even what the question was asking for?
     
  2. jcsd
  3. Nov 3, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, that's exactly right.
     
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