Q8 of 47 Page 1

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

Let the fixed points be A (a + b, b – a), B (a – b, a + b), P(x, y)

Since the variable point P is equidistant from A & B so it must lie on the perpendicular bisector of the line joining A & B


Let the midpoint of AB be M(x, y)


Using Section formula:


M(x, y) =


⇒ M(x, y) = (a , b)


Slope of line AB(m1) =


⇒ m1 =


Slope of line PM(m2) =


From the perpendicular relationship we know m1 × m2 = -1


⇒


⇒ ab –ay = ab – bx


⇒ ay = bx


Answer: Hence Proved


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