point p(x,y)is equidistant from the point A(a-b,a+b) & B(-a-b,a+b),then prove that x-a=0

If a point P(x,y) is equidistant from two points A & B, then P lies on the perpendicular bisector of  AB.

We see that  y coordinates of A & B are the equal. So AB parallel to x axis. So perpendicular bisector is perpendicular to x axis. 
It is given by:  x = [(a-b) +  (-a-b) ] /2
                       x = -b   or   x + b = 0

So kindly recheck the question it ,must be x+b = 0 

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