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

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#### Solution

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

PA = PB

`⇒ PA^2 = PB^2`

`⇒(x-7)^2 +(y-1)^2 = (x-3)^2 +(y-5)^2`

`⇒ x^2 +y^2 -14x-2y +50 = x^2 +y^2 -6x -10y +34`

`⇒ 8x -8y = 16 `

`⇒ x-y =2`

Concept: Distance Formula

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