$A(a, 0)$ is a fixed point and $\theta$ is a parameter such that $0 < \theta < 2 \pi$. If $\mathrm{P}(\mathrm{a} \cos \theta, \mathrm{a} \sin \theta)$ is a point on the circle $\mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2$ and $\mathrm{Q}(\mathrm{b} \sin \theta,-\mathrm{b} \cos \theta)$ is a point on the circle $x^2+y^2=b^2$, then the locus of the centroid of the triangle APQ is

• Correct answer
  A

  a circle with centre at $\left(\frac{\mathrm{a}}{3}, 0\right)$ and radius $\left(\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{3}\right)$
• B

  $a$ circle with centre at $(a, 0)$ and radius $\left(\frac{\sqrt{a^2+b^2}}{3}\right)$
• C

  a parabola with focus at $\left(\frac{\mathrm{a}}{3}, 0\right)$
• D

  a parabola with focus at $(a, 0)$

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