Question

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

Answer 1

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`