If P(x, y) is equidistant from the points A(7,1) and B(3, 5), find the relation between x and y.

According to question-


AP = BP


taking square on both sides, we get-


AP2 = BP2


⇒ (7-x)2 + (1-y)2 = (3-x)2 + (5-y)2


[using distance formula, the distance between points (x1,y1) and (x2,y2) is equal to units.]


⇒ x2 - 14x + 49 + y2 - 2y + 1 = x2 - 6x + 9 + y2 - 10y + 25


⇒ -8x + 8y + 16 = 0


⇒ -8(x-y-2) = 0


⇒ x-y-2 = 0


∴ x-y = 2


This is the required relation between x and y.


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