Find the point on y - axis which is equidistant from point (- 5, - 2) and (3, 2).

Given points are A(- 5, - 2) and B(3, 2).

We need to find a point on y - axis which is equidistant from these points.

Let us assume the point on y - axis be S(0, y).

We know that distance between the points (x₁, y₁) and (x₂, y₂) is .

From the problem,

⇒ SA = SB

⇒ SA² = SB²

⇒ (0 - (- 5))² + (y - (- 2))² = (0 - 3)² + (y - 2)²

⇒ (5)² + (y + 2)² = (- 3)² + (y - 2)²

⇒ 25 + y² + 4y + 4 = 9 + y² - 4y + 4

⇒ 8y = - 16

⇒ y = - 2

∴ The point on y - axis is (0, - 2).