Q. For the curve $y^{n} = a^{n - 1}x$ if the subnormal at any point is a constant, then $n$ is equal to
A) 1
B) 2
C) -2
D) -1
Explanation
(b)
For the curve $y^{n} = a^{n - 1}x$
$ny^{n - 1}y.\frac{dy}{dx} = a^{n - 1}$
$\therefore$Length of subnormal=$y = \frac{dy}{dx}$
$= y \times \frac{a^{n - 1}}{ny^{n - 1}} = \frac{a^{n - 1}}{ny^{n - 2}}$
For constant subnormal, $n$ should be 2
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.