Q. 114.3( 24 Votes )

If the point P(x, y) is equidistant from the points A(5, 1) and B(– 1, 5), prove that 3x = 2y.

Answer :

The point P(x, y) is equidistant from the points A(5, 1) and B(– 1, 5), means PA = PB

By distance formula, as shown below:



PA = √{(5 – x)2 + (1 – y)2}


= √{(25 + x2 – 10x) + (1 + y2 – 2y)}


PA = √{26 + x2 – 10x + y2 – 2y}


PB = √{(– 1 – x)2 + (5 – y)2}


= √{(1 + x2 + 2x + 25 + y2 – 10y)}


PB = √{(26 + x2 + 2x + y2 – 10y)}


Now, PA = PB


Squaring both sides, we get


26 + x2 – 10x + y2 – 2y = 26 + x2 + 2x + y2 – 10y


12x = 8y


3x = 2y


Hence proved.


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