Over the complex projective plane there are only two types of degenerate conics – two different lines, which … See more

Non-degenerate real conics can be classified as ellipses, parabolas, or hyperbolas by the discriminant of the non-homogeneous form , which is the determinant of the matrix
the matrix … See more

Conics, also known as conic sections to emphasize their three-dimensional geometry, arise as the intersection of a plane with a cone. Degeneracy occurs when the plane contains the apex of the cone or when the c… See more

Degenerate conics, as with degenerate algebraic varieties generally, arise as limits of non-degenerate conics, and are important in compactification of moduli spaces of curves.
For exampl… See more

In the complex projective plane, all conics are equivalent, and can degenerate to either two different lines or one double line.
In the real affine plane:
• Hyperbolas can degenerate to two intersectin… See more

A general conic is defined by five points: given five points in general position, there is a unique conic passing through them. If three of these points lie on a line, then the conic is reducible, and may or may not be unique. If n… See more