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Thread: orthogonal trajectory of an ellipse!

  1. February 11th 2009, 10:07 PM #1
    khood
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    orthogonal trajectory of an ellipse!

    Find the orthogonal trajectories of the family of curves.


    I don't know how to begin this!
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  2. February 11th 2009, 11:11 PM #2
    NonCommAlg
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    Quote Originally Posted by khood View Post
    Find the orthogonal trajectories of the family of curves.


    I don't know how to begin this!
    differentiate your curve: x+2yy'=0. replace y' with \frac{-1}{y'} to get the differential equation of the orthogonal trajectories: \frac{y'}{y}=\frac{2}{x}. solve the equation to get: y=cx^2.
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