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Math Help - Orthogonal trajectory problem

  1. #1
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    Orthogonal trajectory problem

    I know this is probably a super easy problem, but I'm not getting it.

    For problems 15-20, find the equation of the orthogonal trajectories to the given family of curves.

    x2+4y2=c

    I used implicit differentiation and I got dy/dx=-x/4y

    I know the slope of the orthagonal trajectory curve will be dy/dx=-1/f(x,y) which is dy/dx=4y/x

    integrating that equation gave me y=x4+k but the answer in the back of my textbook is y=kx4

    not sure why the constant is in the wrong place
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  2. #2
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    Re: Orthogonal trajectory problem

    oops caught my mistake, sorry mods
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