Q. For the curve $xy = c^{2}$ the subnormal at any point varies as
A) $x^{3}$
B) $x^{2}$
C) $y^{3}$
D) $\infty$
Explanation
(c)
Given, $y = \frac{c^{2}}{x}$
$\Rightarrow \ \ \ \frac{dy}{dx} = c^{2}\left( - \frac{1}{x^{2}} \right)$
$\therefore$ Subnormal at any point $= y.\frac{dy}{dx}$
$= y \times \left( - \frac{c^{2}}{x^{2}} \right) = \frac{- y^{3}}{c^{2}}$
$\therefore$ Subnormal $\propto y^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.