Parabola vs. Ellipse — 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 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.

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 conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone.

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.

The locus of points for which the sum of the distances from each point to two fixed points is equal.

(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

Ellipsis.

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

(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. Category:en:Curves

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.

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

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

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.

Omission. See Ellipsis.

The elliptical orbit of a planet.

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