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We have, AP = BP Squaring both sides, we get {AP}^{2} = {BP}^{2} {(2 - x)}^{2} + {(5 - y)}^{2} + {(8 - z)}^{2} = {(3 - x)}^{2} + {(7 - y)}^{2} + {(2 - z)}^{2} x^{2} + 4 - 4 x + 25 + y^{2} - 10 y + z^{2} + 64 - 16 z = 9 + x^{2} - 6 x + 49 + y^{2} - 14 y + 4 + z^{2} - 4 z 2 x + 4 y - 12 z + 31 = 0

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