if the points 5 4 and x y are equidistant from

Question

If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x² + y² - 8x - 10y +39 = 0.

Ans :  AP = PB AP² = PB²

(5 - 4)² + (4 - 5)² = (x - 4)² + (y - 5)²

1 + 1 = x² - 8x + 16 + y² - 10y + 25 x² + y² - 8x - 10y + 41 - 2 = 0

x² + y² - 8x - 10y + 39 = 0