Q214 / 270 · NDA 2012 (Phase 2) · Mathematics

If $x^m+y^m=1$ such that $\frac{d y}{d x}=-\frac{x}{y}$, then what should be the value of $m$ ?

  • A
    0
  • B
    1
  • Correct answer
    C
    2
  • D
    None of the above

Solution

$\begin{aligned} & x^m+y^m=1 \\ & m x^{m-1}+m y^{m-1} \cdot \frac{d y}{d x}=0\end{aligned}$ $\frac{d y}{d x}=\left(-\frac{x}{y}\right)^{m-1}$ $\begin{aligned} & \quad\left(-\frac{x}{y}\right)^1=\left(-\frac{x}{y}\right)^{m-1} \\ & \Rightarrow m-1=1 \quad \therefore m=2 .\end{aligned}$

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

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