parabola

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. 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.

Century Dictionary and Cyclopedia

1. n. Same as parabole.
2. n. A curve commonly defined as the intersection of a cone with a Plane parallel with its side. The name is derived from the following property. Let the figure represent the cone. Let ABG be the triangle through the axis of the cone. Let DE be a line perpendicular to this triangle, cutting BG in H. Let the cone be cut by a plane through DE parallel to AG, so that the intersection with the cone will be the curve called the parabola. Let Z be the point where this curve cuts AB. Then the line ZH is called by Apollonius the diameter of the parabola, or the principal diameter, or the diameter from generation; it is now called the axis. From Z draw ZT at right angles to ZH and in the plane of ZH and AB, of such a length as to make ZT: ZA: BG: A B. AG. This line ZT is called the latus rectum; it is now also called the parameter. Now take any point whatever, as K, on the curve. From it draw KL parallel to DE meeting the diameter in L. ZL is called the abscissa. If now, on ZL as a base, we erect a rectangle equal in area to the square on KL, the other side of this rectangle may be precisely superposed upon the latus rectum, ZT. This property constitutes the best practical definition of the parabola. If a similar construction were made in the case of the ellipse, the side of the rectangle would fall short of the latus rectum; in the case of the hyperbola, would surpass it. The modern scientific definition of the parabola is that it is that plane curve of the second order which is tangent to the line at infinity. The parabola is also frequently defined as the curve which is everywhere equally distant from a fixed point called its focus, and from a fixed line called its directrix. The normal to a parabola at every point on the curve bisects the angle between the line parallel to the axis and the line to the focus. See also cuts under conic.
3. n. By extension, any algebraical curve, or branch of a curve, having the line at infinity as a real tangent. Such a curve runs off to infinity without approximating to an asymptote. If the branch has an asymptote at one end but not at the other, it is not commonly termed a parabola.

Wiktionary

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

GNU Webster's 1913

1. n. 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.
2. n. One of a group of curves defined by the equation y = axn where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = 3/2. See under cubical, and semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.

WordNet 3.0

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