Definitions for conic section
con·ic sec·tion

Princeton's WordNetRate this definition:0.0 / 0 votes

1. conic section, conicnoun

   (geometry) a curve generated by the intersection of a plane and a circular cone

WiktionaryRate this definition:0.0 / 0 votes

1. conic sectionnoun

   Any of the four distinct shapes that are the intersections of a cone with a plane, namely the circle, ellipse, parabola and hyperbola.

WikipediaRate this definition:0.0 / 0 votes

1. Conic section

   A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes called as a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set of those points whose distances to some particular point, called a focus, and some particular line, called a directrix, are in a fixed ratio, called the eccentricity. The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is, as the set of points whose coordinates satisfy a quadratic equation in two variables which can be written in the form A x 2 + B x y + C y 2 + D x + E y + F = 0. {\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0.} The geometric properties of the conic can be deduced from its equation. In the Euclidean plane, the three types of conic sections appear quite different, but share many properties. By extending the Euclidean plane to include a line at infinity, obtaining a projective plane, the apparent difference vanishes: the branches of a hyperbola meet in two points at infinity, making it a single closed curve; and the two ends of a parabola meet to make it a closed curve tangent to the line at infinity. Further extension, by expanding the real coordinates to admit complex coordinates, provides the means to see this unification algebraically.

ChatGPTRate this definition:0.0 / 0 votes

1. conic section

   A conic section is a curve obtained as the intersection of the surface of a cone with a plane. The four types of conic sections are the circle, ellipse, parabola, and hyperbola. The type of conic is determined by the angle of the plane intersects with the cone.

WikidataRate this definition:0.0 / 0 votes

1. Conic section

   In mathematics, a conic section is a curve obtained as the intersection of a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. There are a number of other geometric definitions possible. One of the most useful, in that it involves only the plane, is that a conic consists of those points whose distances to some point, called a focus, and some line, called a directrix, are in a fixed ratio, called the eccentricity. Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section. The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas. In the focus-directrix definition of a conic the circle is a limiting case with eccentricity 0. In modern geometry certain degenerate cases, such as the union of two lines, are included as conics as well.

Matched Categories

1. • Geometry
   • Plane Figure

How to pronounce conic section?

1. Alex

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   Daniel

   British

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How to say conic section in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of conic section in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of conic section in Pythagorean Numerology is: 3

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=conic section
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Conic_Section
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Conic_Section
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=conic section