About: Degenerate conic

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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 complex numbers (or more generally over an algebraically closed field) as the product of two linear polynomials. Using the alternative definition of the conic as the intersection in three-dimensional space of a plane and a double cone, a conic is degenerate if the plane goes through the vertex of the cones.

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rdfs:label	Sección cónica degenerada (es) Degenerate conic (en)
rdfs:comment	Se denomina sección cónica degenerada a la intersección de un cono circular recto de dos hojas con un plano que pasa por su vértice. Se clasifican en tres tipos: punto, recta y par de rectas. (es) 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 complex numbers (or more generally over an algebraically closed field) as the product of two linear polynomials. Using the alternative definition of the conic as the intersection in three-dimensional space of a plane and a double cone, a conic is degenerate if the plane goes through the vertex of the cones. (en)
foaf:depiction
dcterms:subject	Conic sections
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Link from a Wikipage to another Wikipage	Projective transformation Quartic function Algebraically closed field Apex (geometry) Pencil (mathematics) Resolvent cubic Line segment Orbit Complex number Cone Cone (geometry) Conic section Elliptic orbit General position Circle Geometry Multinomial coefficient Linear system of conics Compactification (mathematics) Complex conjugate line Pappus's hexagon theorem Parallel postulate Plane (geometry) Three-dimensional space Line at infinity Affine transformation Algebraic varieties Conic sections Pascal's theorem Focus (geometry) Hyperbola Plane curve Affine plane Trapezoid Moduli of algebraic curves The American Mathematical Monthly Discriminant General linear position Mathematical Association of America Parallelogram Five points determine a conic Polynomial equation Conic Irreducible variety
Link from a Wikipage to an external page	https://archive.org/details/matricestransfor0000pett http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node28.html http://users.ipfw.edu/CoffmanA/pov/lsoc.html $https://web.archive.org/web/20120224203002/http:/www.ipfw.edu/math/Coffman/pov/conic1.gif$
sameAs	Degenerate conic Degenerate conic Degenerate conic Degenerate conic Degenerate conic
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has abstract	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 complex numbers (or more generally over an algebraically closed field) as the product of two linear polynomials. Using the alternative definition of the conic as the intersection in three-dimensional space of a plane and a double cone, a conic is degenerate if the plane goes through the vertex of the cones. In the real plane, a degenerate conic can be two lines that may or may not be parallel, a single line (either two coinciding lines or the union of a line and the line at infinity), a single point (in fact, two complex conjugate lines), or the null set (twice the line at infinity or two parallel complex conjugate lines). All these degenerate conics may occur in pencils of conics. That is, if two real non-degenerated conics are defined by quadratic polynomial equations f = 0 and g = 0, the conics of equations af + bg = 0 form a pencil, which contains one or three degenerate conics. For any degenerate conic in the real plane, one may choose f and g so that the given degenerate conic belongs to the pencil they determine. (en) Se denomina sección cónica degenerada a la intersección de un cono circular recto de dos hojas con un plano que pasa por su vértice. Se clasifican en tres tipos: punto, recta y par de rectas. (es)
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foaf:isPrimaryTopicOf	wikipedia-en:Degenerate_conic
is Link from a Wikipage to another Wikipage of	Quartic function Pencil (geometry) Line segment

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