Mathematics - Calculus
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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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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.
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