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

If the point P(x,y) is equidistant from the points A(a+b,b-a) and B(a-

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
Answer» Distace between the points (x, y) and (a+b, b-a) & (a-b, a+b) is equal\xa0⇒\xa0√{[x - (a + b)]2\xa0+ [y - (b -a)]2} =\xa0√{x - (a - b)]2\xa0+ [y - (a + b)]2}⇒ x2\xa0+ (a + b)2\xa0- 2x(a + b) + y2\xa0+ (b - a)2\xa0- 2y(b - a) = x2\xa0+ (a - b)2\xa0- 2x(a - b) + y2\xa0+ (a + b)2\xa0- 2y(a + b)⇒ -2ax - 2bx - 2by + 2ay = - 2ax + 2bx - 2ay - 2by⇒\xa0ay - bx = bx - ay⇒ 2ay = 2bx⇒ bx = ayHence proved.