Question

The value of $P$ such that the length of subtangent 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, $y=e^{Px}+Px$

Therefore, $\frac{dy}{dx}=P{e}^{px}+P$

${\left(\frac{dy}{dx}\right)}_{(0,1)}=2P$

Subtangent $=\left|y\frac{dx}{dy}\right|$, subnormal $=\left|y\frac{dy}{dx}\right|$

Given, Subtangent $=$ Subnormal

$\Rightarrow \frac{dy}{dx}=\pm 1$

$\Rightarrow 2p=\pm 1$

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