Parabola vs. Hyperbola

Parabolanoun

(geometry) The conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix).

Parabolanoun

(rhetoric) The explicit drawing of a parallel between two essentially dissimilar things, especially with a moral or didactic purpose. A parable.

Parabolanoun

A kind of curve; one of the conic sections formed by the intersection of the surface of a cone with a plane parallel to one of its sides. It is a curve, any point of which is equally distant from a fixed point, called the focus, and a fixed straight line, called the directrix. See Focus.

Parabolanoun

a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve

Parabolanoun

a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Hyperbolanoun

(geometry) A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone.

Hyperbolanoun

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.

Hyperbolanoun

an open curve formed by a plane that cuts the base of a right circular cone

Hyperbolanoun

a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

Hyperbolanoun

the pair of hyperbolas formed by the intersection of a plane with two equal cones on opposite sides of the same vertex.

Hyperbola

In mathematics, a hyperbola (listen) (adjective form hyperbolic, listen) (plural hyperbolas, or hyperbolae (listen)) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.