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Calc HW help orthogonal lines

  1. Oct 9, 2007 #1
    1. The problem statement, all variables and given/known data
    Two curves intersect orthogonally when their tangent lines at each point of intersection are perpendicular. Suppose C is a positive number. The curves y=Cx^2 and y=(1/x^2) intersect twice. Find C so that the curves intersect orthogonally. For that value of C, sketch both curves when -2 < x < 2 and 0 < x < 4

    2. Relevant equations

    3. The attempt at a solution

    The tangent line at the the other equation (y=Cx^2) must be the opposite reciprocal of the tangent line y'=(-2/x^3), therefore it must =(x^3/2) this has to equal the derivative of the equation y=(Cx^2) for this equation to have this derivative C must = (x^2/8) because when subsituted into the equation y=(Cx^2)you get y=(x^2/8)(x^2) which is equal to y=(x^4/8) when you find its derivative you get y'= (x^3/2).
    I'm not sure if im going about doing this correctly if anyone can point me in the right direction please give me anything you have to offer. thanks
  2. jcsd
  3. Oct 9, 2007 #2


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    At which point(s) do they intersect?
  4. Oct 9, 2007 #3
    (1.4,.5), (-1.4,.5)
  5. Oct 11, 2007 #4


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    How is it that these points do not involve terms with C? (I don't understand how or why they are independent of C.)
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