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Question

The orthogonal trajectories of the family of curves an1y=xn are given by

A
xn+n2y =constant
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B
ny2+x2 =constant
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C
n2x+yn=constant
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D
n2xyn =constant
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Solution

The correct option is B ny2+x2 =constant

Differentiating, we have an1dydx=nxn1an1=nxn1dxdy
Putting this value in the given equation, we have nxn1dxdyy=xn
Replacing dydxby dydy, we have ny=xdxdy
nydy+xdx=0ny2+x2 =constant. Which is the required family of orthogonal trajectories.

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