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.

Source: Webster's Revised Unabridged Dictionary (1913)