Prove that x2 + y2 - 8x - 10y +39 = 0, Mathematics

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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

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