English definition of Hyperbola

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Definition of hyperbola

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Hyperbola (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. o

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Hyperboliform :: Hyperboliform (a.) Having the form, or nearly the form, of an hyperbola..

Hyperbola :: Hyperbola (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. o

Eccentricity :: Eccentricity (n.) The ratio of the distance between the center and the focus of an ellipse or hyperbola to its semi-transverse axis.

Branch :: Branch (n.) One of the portions of a curve that extends outwards to an indefinitely great distance; as, the branches of an hyperbola..

Lemniscate :: Lemniscate (n.) A curve in the form of the figure 8, with both parts symmetrical, generated by the point in which a tangent to an equilateral hyperbola meets the perpendicular on it drawn from the center..

Hyperboloid :: Hyperboloid (n.) A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface..

Hyper- :: Hyper- () A prefix signifying over, above; as, hyperphysical, hyperthyrion; also, above measure, abnormally great, excessive; as, hyperaemia, hyperbola, hypercritical, hypersecretion..

Hyperboloid :: Hyperboloid (a.) Having some property that belongs to an hyperboloid or hyperbola.

Hyperbolically :: Hyperbolically (adv.) In the form of an hyperbola.

Hyperbolical :: Hyperbolical (a.) Belonging to the hyperbola; having the nature of the hyperbola.

Indicatrix :: Indicatrix (n.) A certain conic section supposed to be drawn in the tangent plane to any surface, and used to determine the accidents of curvature of the surface at the point of contact. The curve is similar to the intersection of the surface with a parallel to the tangent plane and indefinitely near it. It is an ellipse when the curvature is synclastic, and an hyperbola when the curvature is anticlastic..

Parameter :: Parameter (n.) Specifically (Conic Sections), in the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate..