$\mathrm{A}(5,3), \mathrm{B}(3,-2), \mathrm{C}(2,-1)$ are three points. If $\mathrm{P}$ is a variable point such that the area of the quadrilateral $\mathrm{PABC}$ is 10 sq. units, then the locus of $\mathrm{P}$ is

• Correct answer
  A

  $16 x^2-24 x y+9 y^2-144 x+108 y-76=0$
• B

  $16 x^2-24 x y+9 y^2+144 x-108 y-76=0$
• C

  $16 x^2-24 x y+9 y^2-144 x+108 y+76=0$
• D

  $16 x^2-24 x y+9 y^2+144 x-108 y+76=0$

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