n. a conic section with eccentricity greater than 1, formed by a plane that cuts both bases of a cone; it consists of two branches asymptotic to two intersecting fixed lines, and has two foci. When symmetrical about the coordinate axes it has equation: where the transverse axis coincides with the x-axis, the conjugate axis lies on the y-axis, 2a is the distance between the two intersections with the x-axis, and b = √(e² - 1), where e is the eccentricity. Its parametric equations are
x = asecθ, y = btanθ
and, as shown in this figure,the general hyperbola has asymptotes y = ±(b/a) x. See also rectangular hyperbola.