Q. The length of the subtangent at (2,2) to the curve $x^{5} = 2y^{4}\$is
A) $\frac{5}{2}$
B) $\frac{8}{5}$
C) $\frac{2}{5}$
D) $\frac{5}{8}$
Explanation
(b)
Given, $2y^{4} = x^{5}$
$\Rightarrow \ \ \ \ \ 8y^{3}\frac{dy}{dx} = 5x^{4}$
$\Rightarrow \ \ \ \ \left( \frac{dy}{dx} \right)_{(2,\ 2)} = \frac{5(2)^{4}}{8(2)^{3}} = \frac{5}{4}$
$\therefore$ Length of subtangent$= \frac{y}{dy/dx} = \frac{2}{5/4} = \frac{8}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.