# parabola

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## parabola

(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.
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.

## parabola

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

## Parabola

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.

## parabola

[pə′rab·ə·lə]
(mathematics)
The plane curve given by an equation of the form y = ax 2+ bx + c.

## parabola

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 ?
En este libro se recogen una serie de meditaciones sobre las parabolas evangelicas.
Hillis Miller faz uma analogia entre a narrativa de O coracao das trevas e a parabola, tendo como modelo a parabola biblica.
Aunque Parabolas del equilibrio no invita o desafia, ni busca hacer revolucion de conciencias (no hay muralismo), quiza sea una de las fotografias mas fieles e ironicas de nuestro tiempo: el cuerpo es una luz del paraiso recobrado.
Figure 2 shows a minimal response to each of the three tasks, with only one example provided for each type of parabola in Part A, partial generalisation using features of positive parabolas, and one example horizontal line for each type in Part C.
By equating the equation of the straight line and the equations of the parabolas, we obtain the points of intersection
la Iglesia propone, en un lenguaje--por cierto testimonial--analogo al de las parabolas, mas cercano asi al estilo narrativo, a Jesucristo como profecia de autentica humanidad.
Neste contexto, o objetivo deste artigo e apresentar uma nova abordagem para o metodo geometrico utilizando o indice da parabola na geracao de equacoes taper, para estimar o volume de arvores individuais e comparar as estimativas de volume realizadas a partir deste metodo com o volume obtido pela cubagem rigorosa de clones de eucalipto plantados em tres sitios florestais.
Na tradicao dos profetas do Velho Testamento, por exemplo, temos algumas parabolas, como a da ovelha/vaca e o pobre, que foi narrada pelo profeta Nata para repreender Davi, no segundo livro do profeta Samuel, no capitulo 12, a qual transcreveremos a seguir junto com o contexto que lhe sucede:
The effect is created by the plane shooting up to an altitude of 32,000 feet and then executing a series of aerobatic maneuvers called parabolas - essentially climbing and falling in arcs about 15 times.
Marcial Fernandez (abre el debate): Segun se puede inferir de Vicente Lenero --autoridad en el tema--, las parabolas de Jesus son microrrelatos con final abierto.
Las parabolas de Jesus reflejan de un modo admirable el ambiente y la vida cotidiana de la Palestina en los anos 30.
Appropriate for community college courses, this textbook explains how to solve algebraic equations and formulas, factor trinomials, add rational expressions and radicals, and graph parabolas, ellipses, and functions.

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