A plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone. It is the locus of points for which the difference of the distances from two given points is a constant.
The path of a point that moves so that the difference of its distances from two fixed points, the foci, is constant; curve formed by the section of a cone cut by a plane more steeply inclined than the side of the cone.
A plane curve having two separate parts or branches, formed when two cones that point toward one another are intersected by a plane that is parallel to the axes of the cones.
New Latin from Greek huperbolēa throwing beyond, excess (from the relationship between the line joining the vertices of a conic and the line through its focus and parallel to its directrix)hyperbole
The hyperbola which has for its transverse and conjugate axes the transverse and conjugate axes of another hyperbola is said to be the conjugate hyperbola.
But Landen's capital discovery is that of the theorem known by his name (obtained in its complete form in the memoir of 1775, and reproduced in the first volume of the Mathematical Memoirs) for the expression of the arc of an hyperbola in terms of two elliptic arcs.
The same name is also given to the first positive pedal of any central conic. When the conic is a rectangular hyperbola, the curve is the lemniscate of Bernoulli previously described.
it appears that the orbit is an effipse, parabola or hyperbola according as v2 is less than, equal to, or greater than 2/sir.
Referred to the asymptotes as axes the general equation becomes xy 2 obviously the axes are oblique in the general hyperbola and rectangular in the rectangular hyperbola.