If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x^{2} + y^{2} - 8x - 10y +39 = 0.
Ans : AP = PB AP^{2} = PB^{2}
(5 - 4)^{2} + (4 - 5)^{2} = (x - 4)^{2} + (y - 5)^{2}
1 + 1 = x^{2} - 8x + 16 + y^{2} - 10y + 25 x^{2} + y^{2} - 8x - 10y + 41 - 2 = 0
x^{2} + y^{2} - 8x - 10y + 39 = 0