Q109 / 160 · AP EAMCET 2008 · Mathematics
The length of the subtangent at $(2,2)$ to the curve $x^5=2 y^4$ is
- A$\frac{5}{2}$
- Correct answerB$\frac{8}{5}$
- C$\frac{2}{5}$
- D$\frac{5}{8}$
Solution
Given that,
$$
2 y^4=x^5
$$
On differentiating w.r.t. $x$, we get
$$
\begin{gathered}
8 y^3 \frac{d y}{d x}=5 x^4 \\
\Rightarrow \quad\left(\frac{d y}{d x}\right)_{(2,2)}=\frac{5(2)^4}{8(2)^3}=\frac{5}{4} \\
\therefore \text { Length of subtangent }=\frac{y}{d y / d x} \\
=\frac{2}{5 / 4}=\frac{8}{5}
\end{gathered}
$$
Hence, the correct answer is option: 'B'.