Correct option is (C) (0, -2)
Let \(P(0, y)\) be any point on y-axis.
Let \(A(5,-2)\) and \(B(-3,2)\). Then,
\(P A=P B \)
\( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\)
\((5-0)^{2}+(-2-y)^{2}=(-3-0)^{2}+(2-y)^{2}\)
\((5)^{2}+(-2)^{2}+(y)^{2}-2 \times(-2)(y)=(-3)^{2}+(2)^{2}+(y)^{2}-2 \times 2\times y\)
\(25+4+y^{2}+4 y=9+4+y^{2}-4 y\)
\( 4 y+4 y=9-25\)
\(8y=-16\)
\(y = \frac{-16}8 = -2\)
Therefore, the required point is \((0,-2)\).
