1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook