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Implicitly difined curve, fine point with given slope.

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Here is the full question.
    Consider a curve defined by 2y^3 + 6x^2y - 12x^2 + 6y = 1 and dy/dx = (4x-2xy)/(x^2+y^2+1).

    The line through the origin with slope -1 is tangent to the curve at point P. Find the x - coordinate and y - coordinate of point P.

    2. Relevant equations

    2y^3 + 6x^2y - 12x^2 + 6y = 1
    dy/dx = (4x-2xy)/(x^2+y^2+1)

    3. The attempt at a solution

    The equation for the line through (o,o) with slope -1 which I found to be y = -x. I tried to plug -x back into original equation but came up with a weird expression for y.

    Thanks for any help in advance.
    Last edited: Feb 9, 2010
  2. jcsd
  3. Feb 9, 2010 #2


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    Science Advisor
    Homework Helper

    Weird in what way? Sure, the tangent line is y=(-x). You also have dy/dx=(-1), right? What's so weird about that? You'll have to tell us.
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