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    I need to find the orthogonal trajectories of the family of curves, y = 1/(x+c) where k is an arbitrary constant.

    So far, I had figured on c = (1/y) - x

    m1 = -1/(x^2 + (1/y) - x)
    m2 = x^2 + (1/y) - x

    I don't know how to figure beyond that. Probably because those were calculated wrong. Please show me how it's done. Thank you.

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    https://brainmass.com/math/basic-calculus/orthogonal-trajectories-family-curves-258003

    Solution Preview

    y = 1/(x + c)
    Differentiating with respect to x, we get dy/dx = -1/(x + c)^2
    The ...

    Solution Summary

    Orthogonal trajectories of a family of curves is determined. A complete, neat and step-by-step solution is provided in the attached file.

    $2.49

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