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Orthogonal Trajectory Problem

  1. Jul 16, 2006 #1
    I am working on this problem, and have a simple question.

    Determine the orthogonal trajectory of
    [tex] x^p + Cy^p = 1 [/tex]
    where p = constant.

    I start out by taking the derivative with respect to x. My question is this. does
    [tex] Cy^p [/tex] become [tex] Cpy^{p-1} [/tex] or [tex] C_1y^{p-1}[/tex] ?

    Last edited: Jul 16, 2006
  2. jcsd
  3. Jul 16, 2006 #2


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    Science Advisor

    C1?? There isn't any "C1" in your original formula!

    The derivative of yp with respect to y is pyp-1. The derivative of Cyp with respect to y is Cpyp-1. By the chail law, the derivative of Cyp is [itex]Cpy^{p-1}\frac{dy}{dx}[/itex]. Solve the resulting equation for [itex]\frac{dy}{dx}[/itex] to find the slope of the tangent line to the original trajectory at each point.
  4. Jul 16, 2006 #3
    If p is a constant and C is a constant isn't
    just another constant? Isn't
    [tex]C_1y^{p-1}\frac{dy} {dx} [/tex]
    the same as what you have?

    Thanks for pointing out the chain rule, I missed that.
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