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Degenerate conic - Wikipedia
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 cone degenerates to a cylinder and the plane is parallel to the axis of the cylinder. See Conic … See more
In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. This means that the defining equation is factorable over the 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
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 projective transformation into any other degenerate … 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
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WEBLearn the definitions, properties and types of conic sections, including degenerate and non-degenerate conics. Find out how to classify conics based on the value of the discriminant of the equation and see …
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WEBLearn what conic sections are, how they are formed by intersecting a cone with a plane, and how they are classified by their eccentricity. Explore the features, graphs, and applications of parabolas, ellipses, …
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WEBFeb 18, 2022 · We’ll start here with common instances of the phenomenon, in conic sections, pursuing the elusive case of a pair of parallel lines. Next time we’ll look at how properties of conics apply to degenerate cases, …
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