Correct option is (C) (0, -2)
Let the coordinates of the point on y-axis be P(0, y).
Let the given points be A(5, -2) and B(-3, 2).
If is given that PA = PB
\(\Rightarrow \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
\(\Rightarrow \sqrt{\left(0-5)^2+(y-(-2)\right)^2} =\sqrt{\left.(0-(-3))^2+(y+2)\right)^2} \)
\(\Rightarrow \sqrt{(5)^2+(y+2)^2} =\sqrt{(3)^2+(y+2)^2}\)
\(\Rightarrow 25+(y+2)^2 =9+(y+2)^2\)
\(\Rightarrow 25+y^2+4+4 y =9+y^2+4-4 y\)
\(\Rightarrow y^2+4 y+29 =y^2-4 y+13\)
\(\Rightarrow 4 y+4 y =13-29\)
\(\Rightarrow 8 y =-16 \)
\(\therefore y =\frac{-16}{8}=-2\)
Thus, the coordinates of the required point is (0, -2).
