Parabola vs. Paraboloid — What's the Difference?

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.

In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry.

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.

A surface having parabolic sections parallel to a single coordinate axis and elliptic or circular sections perpendicular to that axis.

A plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the locus of points equidistant from a fixed line and a fixed point not on the line.

(mathematics) A surface having a parabolic cross section parallel to an axis, and circular or elliptical cross section perpendicular to the axis; especially the surface of revolution of a parabola. Category:en:Surfaces

(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). Category:en:Functions Category:en:Curves

The solid generated by the rotation of a parabola about its axis; any surface of the second order whose sections by planes parallel to a given line are parabolas.

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

A surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis

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.

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