Definition of Hyperbolas. Meaning of Hyperbolas. Synonyms of Hyperbolas

Here you will find one or more explanations in English for the word Hyperbolas. Also in the bottom left of the page several parts of wikipedia pages related to the word Hyperbolas and, of course, Hyperbolas synonyms and on the right images related to the word Hyperbolas.

Definition of Hyperbolas

Hyperbola
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.

Meaning of Hyperbolas from wikipedia

- of a hyperbola is the Klein four-group. The rectangular hyperbolas xy = constant admit group actions by squeeze mappings which have the hyperbolas as invariant...
- unit hyperbola requires the conjugate hyperbola y 2 − x 2 = 1 {\displaystyle y^{2}-x^{2}=1} to complement it in the plane. This pair of hyperbolas share...
- ellipses and hyperbolas have two foci, there are confocal ellipses, confocal hyperbolas and confocal mixtures of ellipses and hyperbolas. In the mixture...
- sometimes called the numerical eccentricity. In the case of ellipses and hyperbolas the linear eccentricity is sometimes called the half-focal separation...
- diameters of both hyperbolas." "The two hyperbolas so constructed are called conjugate hyperbolas, and [the] last drawn is the hyperbola conjugate to the...
- Retrieved 2007-09-06. "The Geometry of Orbits: Ellipses, Parabolas, and Hyperbolas". www.bogan.ca. "7.1 Alternative Characterization". Archived from the...
- the complex coordinate plane C2, ellipses and hyperbolas are not distinct: one may consider a hyperbola as an ellipse with an imaginary axis length. For...
- {\displaystyle x^{2}+y^{2}=a^{2}+b^{2}} (see below), The orthoptic of a hyperbola x 2 a 2 − y 2 b 2 = 1 ,   a > b {\displaystyle {\tfrac {x^{2}}{a^{2}}}-{\tfrac...
- [citation needed] By 2019, i-Space had successfully launched the Hyperbola-1S and Hyperbola-1Z single-stage solid-propellant test rockets into space on suborbital...
- hyperbolic orthogonality is the relation of conjugate diameters of rectangular hyperbolas. The placement of tie rods reinforcing a square ****embly of girders is...