Assuming that you are, in fact, talking about the equation for a circle, there's another reason why the equation x^2 + y^2 = 0 can't give you the center of the circle at the origin.
If we subtract x^2 from both sides of the equation, we see that y^2 = -(x^2). But no real number except zero for both x and y will make that equation true. And those values will give you the origin (0,0) as a solution, but you only have a point--as the earlier answer states, no circle.
What if the values of x and y are not zero? y^2 still has to have the same value as the opposite of x^2. We know that squaring a number will never result in a negative number, so the only non-zero values of x and y will be ones in which one of the variables is real and the other is imaginary. And although we may use our imagination to conjure up a circle, a circle is not composed of imaginary values.
This equation cannot be the equation for the origin, since, x^2 + y^2= the radious of a circle squared. If the radious of a circle squared is zero, then the circle doesn`t exist...