How would I go about showing that the equation (x-a)^2 = x^2 + y^2 defines a parabola? If I put the equation in terms of y, I get y = sqrt(a^2 - 2xa), which is not a parabola. I've found the derivative to be y' = -a/y, but I don't think that proves anything. If anyone has any ideas, I'd really appreciate them! Thanks.
PS 'a' is a constant.