How to find the orthogonal trajectories — Krista King Math | Online math help

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SOLVED: The orthogonal trajectories of the family of curves y = cx^2 2y^2 = k are given by the equation 2x^2 y^2 = k. Another equation for the orthogonal trajectories is x - ky^2 = 0. The equation x = e^ky represents another set of orthogonal trajectories.

Find the value of n such that the cuves x^n y^n=c1 are the orthogonal trajectories of the family y=(x)/(1-c2 x) . | Numerade