Question

The length of the subtangent at $(2,2)$ to the curve $x^{5}=2 y^{4}$ is

• A. $\frac{5}{2}$
• B. $\frac{8}{5}$
• C. $\frac{2}{5}$
• D. $\frac{5}{8}$

Answer 1

Answer: (B)

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