A straight line passing through a point $(3,2)$ cuts X and Y -axes at the points A and B respectively. If a point P divides AB in the ratio $2: 3$, then the equation of the locus of point P is

• A

  $\frac{9}{x}+\frac{4}{y}=1$
• B

  $9 x+4 y=5 x y$
• Correct answer
  C

  $4 x+9 y=5 x y$
• D

  $\frac{4}{x}+\frac{9}{y}=1$

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