What Is the General Equation of a Parabola and Its Derivation?

[DJ24]

I read a Wikipedia article titled "Parabola" that listed an equation of the form:

Ax² + Bxy + Cy² + Dx + Ey + F = 0

How is this derived? or where did it come from?

 

[jgens]

This probably should be under the General Math section of the forums. The equation that you posted is the general quadratic equation and depending of the values of A, B, and C it can either produce parabolas, ellipses, circles, or hyperbolas (excepting a few degenerate cases). If it is a parabola then B² = 4(A)(C).