Q22 of 66 Page 7

If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.(CBSE 2017)

We know, that distance with two coordinates M(x1, y1) and N(x2, y2) is



As, P(x, y) is equidistant from A(5, 1) and B(-1, 5)


⇒ AP = BP



Squaring both side,


⇒ (x - 5)2 + (y - 1)2 = (x + 1)2 + (y - 5)2


⇒ x2 - 10x + 25 + y2 - 2y + 1 = x2 + 2x + 1 + y2 - 10y + 25


⇒ -10x - 2y = 2x - 10y


⇒ 8y = 12x


⇒ 2y = 3x


Hence Proved

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