Orthogonal Trajectories of a given family of curves

  • Let f(x,y,c) = 0 is the family of curves.
  • Differentiating and eliminating c, we get
    F(x,y,y') = 0, where y' is the slope of the curve.
  • The differential equation of the family of orthogonal curve is given by
    F(x,y,-1/y') = 0



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