1.

If the point P(x, y) is equidistant from the points A (6, -1) and B(2, 3), then find a relation between x and y.

Answer»

By hypothesis

PA = PB

⇒ PA2 = PB2

⇒ (x - 6)2 + (y + 1)2 = (x - 2)2 + (y - 3)

⇒ x2 - 12x + 36 + y2 + 2y + 1 = x2 - 4x + 4 + y2 - 6y + 9

⇒ 8x - 8y = 24

⇒ x - y = 3



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