If $x=t-\sin t, y=1-\cos t$ and $\frac{d^2 y}{d x^2}=-1$ at $t=\mathrm{K}, \mathrm{K}>0$, then $\underset{t \rightarrow \mathrm{~K}}{\operatorname{Lt}} \frac{y}{x}=$

• A

  $\frac{2}{\pi}$
• B

  $\frac{\pi-2}{2}$
• Correct answer
  C

  $\frac{2}{\pi-2}$
• D

  $\frac{\pi}{2}$

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