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(pərăb`ələ), plane curve consisting of all points equidistant from a given fixed point (focus) and a given fixed line (directrix). It is the conic sectionconic section
or conic
, curve formed by the intersection of a plane and a right circular cone (conical surface). The ordinary conic sections are the circle, the ellipse, the parabola, and the hyperbola.
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 cut by a plane parallel to one of the elements of the cone. The axis of a parabola is the line through the focus perpendicular to the directrix. The vertex is the point at which the axis intersects the curve. The latus rectum is the chord through the focus perpendicular to the axis. Examples of this curve are the path of a projectile and the shape of the cross section of a parallel beam reflector.


(pă-rab -ŏ-lă) A type of conic section with an eccentricity equal to one. See also paraboloid.



a curve that is the intersection of a circular cone by a plane parallel to a tangent plane to the cone (Figure 1, a); it thus is a conic section. A parabola can also be defined as the locus of points in a plane (Figure 1, b) such that each point is equidistant from a fixed point F of the plane and from a given line MN; F is called the focus and MN the directrix of the parabola. The line passing through the focus perpendicular to the directrix and directed from the directrix toward the focus is the axis of the parabola. The point at which the axis intersects the parabola is the vertex of the parabola.

Figure 1

Let us choose the coordinate system xOy, as shown in Figure 1, b. The equation of the parabola then takes the form

y2 = 2px

where p is the length of the segment FN and is called the parameter of the parabola. The parabola is a quadratic curve; it is the graph of the quadratic trinomial y = ax2 + bx + c. It extends to infinity and is symmetric with respect to its axis.

If a light source is placed at the focus of a parabola, the rays reflected by the parabola will form a parallel beam, since the angle formed by the normal PR and the straight line PF connecting any point P of the parabola to the focus is equal to the angle that PR forms with a line parallel to the axis. This property of the parabola is used, for example, in projectors.


The plane curve given by an equation of the form y = ax 2+ bx + c.


a conic section formed by the intersection of a cone by a plane parallel to its side. Standard equation: y2 = 4ax, where 2a is the distance between focus and directrix
References in periodicals archive ?
In the Euclidean plane geometry parabola is the locus of points equidistant from a fixed line (directrix) and a fixed point (a focus) not on the line.
Deste modo, vemos que Jesus nao poderia deixar de se utilizar do expediente das parabolas na pregacao do Evangelho, ligando-se, assim, a uma tradicao discursiva do uso de narrativas alegoricas breves com um fundo pedagogizante.
But this plane makes fewer parabolas than astronaut-training runs, which can make up to 60, and there were no green faces as the fliers stepped off the plane.
It is found that proposed approach can take into account the realistic cable profile in much simplified manner when compared to parabolic model where several parabolas are to model the actual profile.
Likewise, knowing that the orbits of the known planets are elliptical (a circle being a special case of that shape), no reasonably intelligent mathematician or astronomer would have wasted time, as the character Alexander does in Chapter XLVI (or 46), trying to fit parabolas to data observed for that "lost star".
Looking to the sections on parabolas, they each begin with some equivalent of: "This is the equation of a parabola.
To view the wonderful concrete parabolas you need to risk a crick in the neck or having your purse snatched
But my 'coulds' and 'mights' suggest limitations rather than parabolas of possibilities.
Wunderkind Yannick Nezet-Seguin, leading his Orchestre Metropolitain, fashioned many expressive parabolas, but too often at the expense of forward motion.
The second proposition is that the ratio of the areas of two portions of the parabola is equal to the ratio of the areas of the triangles beneath these portions of the parabolas.
He's identified almost everything in the universe as the vital element - but to my knowledge has never once mentioned triangles and parabolas.