Let $z=x+i y$ and $\mathrm{P}(x, y)$ be a point on the Argand plane. If $z$ satisfies the condition $\operatorname{Arg}\left(\frac{z-3 i}{z+2 i}\right)=\frac{\pi}{4}$ then the locus of P is

• A

  $x^2+y^2-y-6=0,(x, y) \neq(0,-2)$
• B

  $x^2+y^2-x-y-6=0,(x, y) \neq(0,-2)$
• Correct answer
  C

  $x^2+y^2+5 x-y-6=0,(x, y) \neq(0,-2)$
• D

  $x^2+y^2+x-y-6=0,(x, y) \neq(0,-2)$

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