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in Coordinate Geometry by (47.8k points)
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Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

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Let P(x, y) be equidistant from the points A(7, 1) and B(3, 5).

We are given that AP = BP. So, AP2 = BP2

(x – 7)2 + (y – 1)2 = (x – 3)2 + (y – 5)2

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

x – y = 2

Which is the required relation

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