the set of points in a plane whose distances to two fixed points in the plane have a constant difference; a curve consisting of two distinct and similar branches, formed by the intersection of a plane with a right circular cone when the plane makes a greater angle with the base than does the generator of the cone. Equation:x 2/a 2 − y 2/b 2 = ±1.
a conic section 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. Standard equation: x²/a² – y²/b² = 1 where 2a is the distance between the two intersections with the x-axis and b = a√(e² – 1), where e is the eccentricity
C17: from Greek huperbolē, literally: excess, extravagance, from hyper- + ballein to throw
1660s, from Latinized form of Greek hyperbole "extravagance," literally "a throwing beyond" (see hyperbole). Perhaps so called because the inclination of the plane to the base of the cone exceeds that of the side of the cone.
Pluralhyperbolas or hyperbolae (hī-pûr'bə-lē) 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.