\begin{definition}[Definition:Discriminant of Quadratic Equation in Two Variables]
Consider the '''quadratic equation in $2$ variables''':
:$(1): \quad a x^2 + b y^2 + 2 h x y + 2 g x + 2 f y + c = 0$
where $x$ and $y$ are independent variables.
The '''discriminant''' of $(1)$ is the expression:
:$a b c + 2 f g h - a f^2 - b g^2 - c h^2$
\end{definition}