Q. 104.7( 20 Votes )

If the distances

Answer :

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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