If the points $\mathrm{A}(2,3), \mathrm{B}(3,2)$ form a triangle with a variable point $\mathrm{p}\left(\mathrm{t}, \mathrm{t}^2\right)$, where t is a parameter, then the equation of the locus of the centroid of triangle ABC is

• A

  $9 x^2-30 x-3 y+20=0$
• Correct answer
  B

  $3 x^2-10 x-y+10=0$
• C

  $9 y^2-30 y-3 x+20=0$
• D

  $3 y^2-10 y-x+10=0$

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