Question

The value of ${}^{\prime }{p}^{\prime }$ such that the length of sub tangent and subnormal is equal for the curve $y=e^{px}+px$ at the point $(0,1)$ is

• A. $p=\pm 1$
• B. $p=\pm 2$
• C. $p=\pm \frac{1}{2}$
• D. None of these

Answer 1

Answer: (C)

$p=\pm \frac{1}{2}$

Given, $y=e^{px}+px$

Thus $\frac{d}{dx}=p{e}^{px}+p$ at point $(0,1)=2p$
Subtangent $=\left|y\frac{dy}{dx}\right|,\text{Subnormal}=\left|y\frac{dy}{dx}\right|$
Given, $\text{Subtangent}=\text{Subnormal}$
$\Rightarrow \frac{dy}{dx}=\pm 1$
$\Rightarrow 2p=\pm 1$
$\Rightarrow p=\pm \frac{1}{2}$