The orthogonal trajectories of the family of curves an−1y=xn are given by
Options:
A .  
xn+n2y= constant
B .  
ny2+x2= constant
C .  
n2x+yn= constant
D .  
n2x−yn= constant
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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