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.