A line segment joining a point A on $x$-axis to a point B on $y$-axis is such that $\mathrm{AB}=15$. If P is a point on AB such that $\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{2}{3}$ then the locus of P is

• Correct answer
  A

  $x=9 \cos \theta, y=6 \sin \theta$
• B

  $x=6 \cos \theta, y=9 \sin \theta$
• C

  $x=6 \cos \theta, y=6 \sin \theta$
• D

  $x=9 \cos \theta, y=9 \sin \theta$

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