\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}.