Over the complex projective plane there are only two types of degenerate conics – two different lines, which necessarily intersect in one point, or one double line. Any degenerate conic may be transformed by a 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 … See more

In the complex projective plane, all conics are equivalent, and can degenerate to either two different lines or one double line. See more

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

Degenerate conics, as with degenerate algebraic varieties generally, arise as limits of non-degenerate conics, and are important in 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, … See more