curve consisting of two separate branches (Geometry)
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Hyperbola Definition from Arts & Humanities Dictionaries & Glossaries
Hyperbola Definition from Language, Idioms & Slang Dictionaries & Glossaries
(n.)
A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.
Webster's Revised Unabridged Dictionary (1913), edited by Noah Porter. AboutA curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.
hyperbola
\hy*per"bo*la\ (?), n. [gr. &?;, prop., an overshooting, excess, i. e., of the angle which the cutting plane makes with the base. see hyperbole.] (geom.) a curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. it is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. see focus. if the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. both curves are regarded as branches of the same hyperbola. see illust. of conic section, and focus.
similar words(3)
equilateral hyperbola
nodated hyperbola
legs of an hyperbola
Noun
1. an open curve formed by a plane that cuts the base of a right circular cone
(hypernym) conic section, conic
Hyperbola Definition from Encyclopedia Dictionaries & Glossaries
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror images of each other and resembling two infinite bows. The hyperbola is one of the four kinds of conic section, formed by the intersection of a plane and a cone. The other conic sections are the parabola, the ellipse, and the circle (the circle is a special case of the ellipse). Which conic section is formed depends on the angle the plane makes with the axis of the cone, compared with the angle a line on the surface of the cone makes with the axis of the cone. If the angle between the plane and the axis is less than the angle between the line on the cone and the axis, or if the plane is parallel to the axis, then the conic is a hyperbola.
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Hyperbola Definition from Entertainment & Music Dictionaries & Glossaries
