The equation of the locus of a point which is at a distance of 5 units from a fixed point $(1,4)$ and also from a fixed line $2 x+3 y-1=0$ is

• A

  $9 x^2+12 x y+4 y^2-30 x-108 y+222=0$
• B

  $9 x^2-12 x y+4 y^2-30 x-98 y+220=0$
• C

  $9 x^2+12 x y+4 y^2-22 x-108 y+222=0$
• Correct answer
  D

  $9 x^2-12 x y+4 y^2-22 x-98 y+220=0$

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