The point on the $Y-$axis equidistant from the point $(9,3)$ and $(-5,2),$ is

The correct option is B $(0,\frac{61}{2})$
Let the required point on the $Y-$axis be $(0,k)$

Given, $(0,k)$ is equidistant from $(9,3)$ and $(-5,2),$ then
$\sqrt{(9-0{)}^2+(3-k{)}^2}=\sqrt{(-5-0{)}^2+(2-k{)}^2}\Rightarrow 81+9+k^2-6k=25+4+k^2-4k\Rightarrow -2k=-61\Rightarrow k=\frac{61}{2}$

Hence, required point is $(0,\frac{61}{2})$