The discriminant of the general conic section a x_1^2 + b x_2^2 + c x_3^2 + 2f x_2 x_3 + 2g x_1 x_3 + 2h x_1 x_2 = 0 is defined as Δ = left bracketing bar a | h | g h | b | f g | f | c right bracketing bar = a b c + 2f g h - a f^2 - b g^2 - c h^2. If b = a and g = h = 0, then simplifies to the circle discriminant.

circle discriminant