Points A(5, -2) and B(-3, 2) are equidistance from point P.
Let the coordinates of point are P(0, y)
Using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
⇒ PA = PB
\(\sqrt{(0 - 5)^2 + (y + 2)^2}\) = \(\sqrt{(0 + 3)^2 + (y - 2)^2}\)
On squaring both sides, we get
(0 - 5)2 + (y + 2)2 = (0 + 3)2 + (y - 2)2
⇒ (- 5)2 + (y + 2)2 = (3)2 + (y - 2)2
⇒ 25 + y2 + 4 + 4y = 9 + y2 + 4 – 4y
⇒ 4y + 4y = 9 – 25
⇒ 8y = -16
⇒ y = - 2
Therefore coordinates are (0, -2).