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(C) The condition $	ext{arg}\left(\frac{z-3}{z-2i}ight)=-\frac{\pi}{2}$ implies that the angle subtended by the segment joining $A(3,0)$ and $B(0,2

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

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(C) The condition $	ext{arg}\left(\frac{z-3}{z-2i}ight)=-\frac{\pi}{2}$ implies that the angle subtended by the segment joining $A(3,0)$ and $B(0,2)$ at point $P(x,y)$ is $-\frac{\pi}{2}$.This means $P$ lies on an arc of a circle passing through $A(3,0)$ and $B(0,2)$.Let $z=x+iy$. Then $\frac{z-3}{z-2i} = \frac{(x-3)+iy}{x+i(y-2)} = \frac{((x-3)+iy)(x-i(y-2))}{x^2+(y-2)^2} = \frac{x(x-3)+y(y-2) + i(xy-2x-3y+6-xy+3y)}{x^2+(y-2)^2} = \frac{x^2+y^2-3x-2y + i(6-2x-3y)}{x^2+(y-2)^2}$.For the argument to be $-\frac{\pi}{2}$,the real part must be $0$ and the imaginary part must be negative.Real part: $x^2+y^2-3x-2y=0$,which is a circle passing through $(3,0)$ and $(0,2)$.Imaginary part: $6-2x-3y  6$.The points $(3,0)$ and $(0,2)$ are excluded because the argument is undefined there.Thus,the locus is the arc of the circle $x^2+y^2-3x-2y=0$ where $2x+3y > 6$.

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

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