Find the point on the X-axis which is equidistant from (2, -5) and (-2, 9).

Let the required point on the X-axis be P(x, 0).
As given, P is equidistant from A(2, -5) and B(-2, 9).
∴ PA = PB
⇒ √(x - 2)² + (0 - (-5))² = √(x + 2)² + (0 - 9)²
⇒ (x - 2)² + 25 = (x + 2)² + 81
⇒ x² - 4x + 4 + 25 = x² + 4x + 4 + 81
⇒ -8x = 56
⇒ x = 56 / -8 = -7
∴ Required point on X-axis = (-7, 0)