# parabola

parabola
/peuh rab"euh leuh/, n. Geom.
a plane curve formed by the intersection of a right circular cone with a plane parallel to a generator of the cone; the set of points in a plane that are equidistant from a fixed line and a fixed point in the same plane or in a parallel plane. Equation: y2 = 2px or x2 = 2py. See diag. under conic section.
[1570-80; < NL < Gk parabolé an application. See PARABLE]

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Open curve, one of the conic sections.

It results when a right circular cone intersects a plane that is parallel to an edge of the cone. It is also the path of a point moving so that its distance from a fixed line (directrix) is always equal to its distance from a fixed point (focus). In analytic geometry its equation is y = ax2 + bx + c (a second-degree, or quadratic, polynomial function). Such a curve has the useful property that any line parallel to its axis of symmetry reflects through its focus, and vice versa. Rotating a parabola about its axis produces a surface (paraboloid) with the same reflection property, making it an ideal shape for satellite dishes and reflectors in headlights. Parabolas occur naturally as the paths of projectiles. The shape is also seen in the design of bridges and arches.

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open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. As a plane curve, it may be defined as the path (locus) of a point moving so that its distance from a fixed line (the directrix) is equal to its distance from a fixed point (the focus).

The vertex of the parabola is the point on the curve that is closest to the directrix; it is equidistant from the directrix and the focus. The vertex and the focus determine a line, perpendicular to the directrix, that is the axis of the parabola. The line through the focus parallel to the directrix is the latus rectum (straight side). The parabola is symmetric about its axis, moving farther from the axis as the curve recedes in the direction away from its vertex. Rotation of a parabola about its axis forms a paraboloid (q.v.).

The parabola is the path, neglecting air resistance and rotational effects, of a projectile thrown outward into the air. The parabolic shape also is seen in certain bridges, forming arches.

For a parabola the axis of which is the x axis and with vertex at the origin, the equation is y2 = 2px, in which p is the distance between the directrix and the focus.

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Universalium. 2010.

### См. также в других словарях:

• parabola (1) — {{hw}}{{parabola (1)}{{/hw}}s. f. 1 (mat.) Sezione d un cono circolare retto ottenuta con un piano parallelo a una generatrice | Traiettoria descritta da un proiettile nell aria. 2 (fig.) Modo di procedere di ogni avvenimento, che incomincia a… …   Enciclopedia di italiano

• Parabola — est également le titre d une chanson du groupe américain Tool figurant sur l album Lateralus Parabola est un film belge réalisé par Karim Ouelhaj, sorti le 9 août 2006. Sommaire 1 Synopsis 2 Pour la petite histoire 3 Fiche technique …   Wikipédia en Français

• Parábola — Saltar a navegación, búsqueda Por Parábola podemos referirnos a, Parábola (matemática), la figura geométrica. Parábola (literatura), la figura literaria. Parábolas de Jesús, las parábolas de Jesús contadas en los evangelios. Parabola, canción del …   Wikipedia Español

• parábola — sustantivo femenino 1. Uso/registro: literario. Narración de un hecho inventado de la que se deduce, por comparación o semejanza, una verdad importante o una enseñanza moral: La Biblia enseña con parábolas. La parábola es un género literario muy… …   Diccionario Salamanca de la Lengua Española

• Parabola — Pa*rab o*la, n.; pl. {Parabolas}. [NL., fr. Gr. ?; so called because its axis is parallel to the side of the cone. See {Parable}, and cf. {Parabole}.] (Geom.) (a) A kind of curve; one of the conic sections formed by the intersection of the… …   The Collaborative International Dictionary of English

• parabola —    paràbola    (s.f.) Per parabola è una narrazione di carattere verisimile, avente la scopo di fornire un esempio di paragone. La parabola per antono­masia è quella che si ritrova presso gli scrittori cristiani, nella cui opera essa indica la… …   Dizionario di retorica par stefano arduini & matteo damiani

• parabola — (n.) 1570s, from Gk. parabole parabola, application (see PARABLE (Cf. parable)), so called by Apollonius of Perga c.210 B.C.E. because it is produced by application of a given area to a given straight line. It had a different sense in Pythagorean …   Etymology dictionary

• parábola — (Del lat. parabŏla, y este del gr. παραβολή). 1. f. Narración de un suceso fingido, de que se deduce, por comparación o semejanza, una verdad importante o una enseñanza moral. 2. Geom. Lugar geométrico de los puntos del plano equidistantes de una …   Diccionario de la lengua española

• paràbola — ž 1. {{001f}}knjiž. a. {{001f}}vrsta pjesničke figure; usporedba b. {{001f}}alegorijska priča koja sadrži istinu ili nauk, priča u kojoj se usporedbom i prenesenim značenjem ilustrira moralna ili religiozna ideja (npr. Isusova priča o gorušičinu… …   Veliki rječnik hrvatskoga jezika

• parábola — s. f. 1. Narração alegórica que envolve algum preceito de moral, alguma verdade importante. 2.  [Geometria] Curva plana cujos pontos distam igualmente de um ponto fixo (foco) e de uma reta fixa (diretriz). 3.  [Portugal: Regionalismo] Dobadoura… …   Dicionário da Língua Portuguesa

• parabola — paràbola ž DEFINICIJA 1. knjiž. a. vrsta pjesničke figure; usporedba b. alegorijska priča koja sadrži istinu ili nauk, priča u kojoj se usporedbom i prenesenim značenjem ilustrira moralna ili religiozna ideja (npr. Isusova priča o gorušičinu zrnu …   Hrvatski jezični portal

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