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If a point P(x, y) is equidistant from the points A(6, -1) and B(2, 3), find the relation between x and y.

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Given: Point P(x, y) is equidistant from points A(6, -1) and B(2, 3)

i.e., distance of P from A = distance of P from B

⇒ \(\sqrt{(x-6)^2+(y+1)^2}\)\(\sqrt{(x-2)^2+(y-3)^2}\)

Squaring both sides,

⇒ (x – 6)2 + (y – 1)2 = (x – 2)2 + (y – 3)2

⇒ x2 – 12x + 36 + y2 – 2y + 1 = x2 – 4x + 4 + y2 – 6y + 9

⇒ –12x + 36 + 2y + 1 = – 4x + 4 – 6y + 9

⇒ – 8x + 8y = –24

⇒ x – y = 3

Therefore, x – y = 3 is the required relation.

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