Noun
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 dictionaryA charged tachyon traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in space-time. Source: Internet
A line g drawn from one focus may intersect this circle in two points M and N; perpendiculars to g drawn through these two points are tangent to the hyperbola. Source: Internet
A parabola is a conic section that is tangent to Ω, and a hyperbola is one that crosses Ω twice. Source: Internet
A hyperbola approaches its asymptotes arbitrarily closely as the distance from its center increases, but it never intersects them; however, a degenerate hyperbola consists only of its asymptotes. Source: Internet
A simple way of producing a hyperboloid is to rotate a hyperbola about the axis of its foci or about its symmetry axis perpendicular to the first axis; these rotations produce hyperboloids of two and one sheet, respectively. Source: Internet
Archimedes had written The Quadrature of the Parabola in the third century BC, but a quadrature for the hyperbola eluded all efforts until Saint-Vincent published his results in 1647. Source: Internet