More like: "If A = -x, then x^2 + y^2 = x^2 + (-a^2)". Your minus in "x^2 - a^2" is placed way wrong. Anyway "-x^2 = x^2", becouse "-x * -y = = xy" and "-x * -x = x^2", but not "-(x^2) = x^2". If you take root of each element you would get "-x = x" wich is more philosophical than mathematcal and wayy wrong. Best explaination i can.
A= -y, which means that A^2 is (-y)(-y), or y^2
LPBhacker! you are RIGHT!
Anyway, it's the x^2 + y^2 = x^2 - a^2 part that's wrong. That'd mean that y^2 = -a^2, which is obviously wrong.
@camtech56: x^2 + y^2 *cannot* be factored as (x - y)(x + y). That's x^2 - y^2. You see, (x - y)(x + y) = x*x + x*y - y*x - y*y = x^2 - y^2.