If $P$ is a variable point which is at a distance of 2 units from the line $2 x-3 y+1=0$ and $\sqrt{13}$ units from the point $(5,6)$, then the equation of the locus of P is

• A

  $4 x^2+12 x y-5 y^2-44 x-42 y+245=0$
• Correct answer
  B

  $12 x y-5 y^2-44 x-42 y+243=0$
• C

  $8 x^2+12 x y-5 y^2-44 x-42 y+243=0$
• D

  $12 x y-13 y^2-44 x-42 y+245=0$

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