Q13 of 47 Page 1

If the point P (x, y) is equidistant from the points A (a + b, b - a) and B (a - b, a + b), prove that bx = ay.

A(a + b, b - a), B(a - b, a + b) and P(x, y) are three points.


P is equidistant from A and B


Therefore, PA = PB


Now using distance formula for two points A(x1, y1) and B(x2, y2)




(a + b - x)2 + (b - a - y)2 = (a - b - x)2 + (a + b - y)2




Cancelling terms we get,


- 2bx + 2ay = 2bx - 2ay


- 4bx = - 4ay


bx = ay


Hence Proved.


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