Q7 of 31 Page 1

Find a relation between x & y such that the point P(x,y) is equidistant from the points A(–5,3) and B(7,2).

Given that,


P(x, y) is equidistant from A(–5, 3) and B(7, 2)


⇒ PA = PB [1]


Formula used:


Distance formula: Distance between two point A(x1, y1) and B(x2, y2)



Using the formula in equation [1], we get



Squaring both side,


⇒ (–5 – x)2 + (3 – y)2 = (7 – x)2 + (2 – y)2


⇒ 25 + 10x + x2 + 9 – 6y + y2 = 49 – 14x + x2 + 4 – 8y + y2


⇒ 10x + 14x – 6y + 8y = 49 + 4 – 25 – 9


⇒ 24x + 2y = 19


[Required relation]


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