Question

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. $\frac{5}{8}$

Answer 1

Answer: (B)

$\frac{8}{5}$

Given, $2y^4=x^5$
On differentiating w.r.t. $x$, we get
$8y^3\frac{dy}{dx}=5x^4$
$\Rightarrow {\left(\frac{dy}{dx}\right)}_{(2,2)}=\frac{5(2{)}^4}{8(2{)}^3}=\frac{5}{4}$
$\therefore$ Length of subtangent $=\frac{y}{\frac{dy}{dx}}=\frac{2}{\frac{5}{4}}=\frac{8}{5}$.