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

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

1.	If the points (x,y) is equidistant from the points A(a+b,b-a) and B(a-b,a+b) .prove that bx=ay
Answer» \|PQ\| = \|PR{tex}\\begin{aligned} \\sqrt { [ x - ( a + b ) ] ^ { 2 } + [ y - ( b - a ) ] ^ { 2 } } = \\sqrt { [ x - ( a - b ) ] ^ { 2 } + [ y - ( b + a ) ] ^ { 2 } } \\end{aligned}{/tex}Squaring, we get[x - (a + b)]2 + [y - (b\xa0- a)]2\xa0= [x - (a - b)]2 + [y - (a + b)]2or, [x - (a + b)]2 - [x - a + b]2\xa0= (y - a - b)2 - (y - b + a)2or, (x - a - b + x - a + b) ( x - a - b - x + a - b)= (y - a - b + y - b + a)(y - a - b - y + b - a)or, (2x - 2a) (- 2b) = (2y - 2b) (- 2a)or, (x - a)b = (y - b)aor, bx = ay.Hence Proved.