If the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p, 0 < p < a$ is $x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0$ then $\lambda=$

• A

  $1$
• B

  $-1$
• C

  $-\mathrm{p}$
• Correct answer
  D

  $-2 p$

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