Question

The length of the sub tangent 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

The correct option is B $\frac{8}{5}$

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