Category:Definitions/Discriminants of Conic Sections

This category contains definitions related to Discriminants of Conic Sections.
Related results can be found in Category:Discriminants of Conic Sections.

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:

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