Question
The orthogonal trajectories of the family of curves an−1y=xn are given by
Answer: Option B
:
B
Differentiating, we have an−1dydx=nxn−1⇒an−1=nxn−1dxdy
Putting this value in the given equation, we havenxn−1dxdyy=xn
Replacing dydx by −dxdy we have ny=−xdxdy
⇒nydy+xdx=0⇒ny2+x2=constant. Which is the required family of orthogonal trajectories.
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B
Differentiating, we have an−1dydx=nxn−1⇒an−1=nxn−1dxdy
Putting this value in the given equation, we havenxn−1dxdyy=xn
Replacing dydx by −dxdy we have ny=−xdxdy
⇒nydy+xdx=0⇒ny2+x2=constant. Which is the required family of orthogonal trajectories.
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