Find the point on y - axis which is equidistant from the points A(6, 5) and B(- 4, 3).

Given points are A(6, 5) and B(- 4, 3).

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 - 6)² + (y - 5)² = (0 - (- 4))² + (y - 3)²

⇒ (- 6)² + (y - 5)² = (4)² + (y - 3)²

⇒ 36 + y² - 10y + 25 = 16 + y² - 6y + 9

⇒ 4y = 36

⇒ y = 9

∴ The point on y - axis is (0, 9).