Let $z=x+i y$ represent a point $\mathrm{P}(x, y)$ in the Argand plane. If $z$ satisfies the condition that amplitude of $\frac{z-3}{z-2 i}=-\frac{\pi}{2}$, then the locus of P is

• A

  the circle $x^2+y^2-3 x-2 y=0$
• Correct answer
  B

  the arc of the circle $x^2+y^2-3 x-2 y=0$ intercepted by the diameter $2 x+3 y-6=0$ containing the origin and excluding the points $(3,0)$ and $(0,2)$
• C

  the arc of the circle $x^2+y^2-3 x-2 y=0$ intercepted by the diameter $2 x+3 y-6=0$ not containing the origin and excluding the points $(3,0)$ and $(0,2)$
• D

  the circle $x^2+y^2-3 x-2 y=0$ not containing the point $(0,2)$

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