Q109 / 200 · Manipal (MET) 2013 · Mathematics

The value $P$ such that the length of subtangent and subnormal is equal for the curve $y=e^{P x}+P x$ at the point $(0,1)$ is

  • A
    $P= \pm 1$
  • B
    $P= \pm 2$
  • Correct answer
    C
    $P= \pm \frac{1}{2}$
  • D
    None of these

Solution

$\frac{d y}{d x}=P e^{p x}+P$ $\left(\frac{d y}{d x}\right)_{(0,1)}=2 P$ Subtangent $=\left|y \frac{d x}{d y}\right|$, subnormal $=\left|y \frac{d y}{d x}\right|$ Given; Subtangent = Subnormal $\Rightarrow \frac{d y}{d x}= \pm 1 \Rightarrow 2 p= \pm 1 \Rightarrow p= \pm \frac{1}{2}$

Hence, the correct answer is option: 'C'.

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