Definition:Discriminant of Conic Section

This page is about Discriminant of Conic Section. For other uses, see Discriminant.

It has been suggested that this page or section be merged into Definition:Discriminant of Quadratic Equation in Two Variables. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code.

Definition

Let $K$ be a conic section embedded in a Cartesian plane with the general equation:

$a x^2 + 2 h x y + b y^2 + 2 g x + 2 f y + c = 0$

where $a, b, c, f, g, h \in \R$.

The discriminant of $K$ is defined as the determinant calculated as:

$\Delta = \begin {vmatrix} a & h & g \\ h & b & f \\ g & f & c \end {vmatrix}$

Also see

• Value of Discriminant of Conic Section

• Results about discriminants of conic sections can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): conic (conic section)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): conic (conic section)