The correct option is B ny2+x2 =constant
Differentiating, we have an−1dydx=nxn−1⇒an−1=nxn−1dxdy
Putting this value in the given equation, we have nxn−1dxdyy=xn
Replacing dydxby −dydy, we have ny=−xdxdy
⇒nydy+xdx=0⇒ny2+x2 =constant. Which is the required family of orthogonal trajectories.