Hyperbola vs. Ellipse

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.

Ellipsenoun

(geometry) A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone.

Ellipseverb

(grammar) To remove from a phrase a word which is grammatically needed, but which is clearly understood without having to be stated.

Ellipsenoun

An oval or oblong figure, bounded by a regular curve, which corresponds to an oblique projection of a circle, or an oblique section of a cone through its opposite sides. The greatest diameter of the ellipse is the major axis, and the least diameter is the minor axis. See Conic section, under Conic, and cf. Focus.

Ellipsenoun

Omission. See Ellipsis.

Ellipsenoun

The elliptical orbit of a planet.

Ellipsenoun

a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it;

Ellipse

In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same.