If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b), then which of the following conditions is true:

Given, PA = PB or (PA)² = (PB)²
(a + b – x)² + (b – a – y)² = (a – b – x)² + (a + b – y)²
or, (a + b)² + x² – 2ax – 25x + (b – a)² + y² – 2by + 2ay

Or,  (a – b)² + x² – 2ax + 2bx + (a + b)² + y² – 2ay – 2by
or,  4ay = 4bx

 or bx = ay