parabola

parabolaAny point on a parabola is the same distance from the directrix as it is from the focus (F). AC equals CF and BD equals DF.

pa·rab·o·la

P0056400 (pə-răb′ə-lə)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.

[New Latin, from Greek parabolē, comparison, application, parabola (from the relationship between the line joining the vertices of a conic and the line through its focus and parallel to its directrix), from paraballein, to compare; see parable.]

parabola

(pəˈræbələ) n (Mathematics) 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[C16: via New Latin from Greek parabolē a setting alongside; see parable]

pa•rab•o•la

(pəˈræb ə lə)

n., pl. -las. 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. See also diag. at conic section. [1570–80; < New Latin < Greek parabolḗ an application]

parabolaThe parabola at left is formed by graphing the function y = x².

pa·rab·o·la

(pə-răb′ə-lə) The curve formed by the set of points in a plane that are all equally distant from both a given line (called the directrix) and a given point (called the focus) that is not on the line.

Thesaurus

Noun

parabola - a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curveconic, conic section - (geometry) a curve generated by the intersection of a plane and a circular cone

Translations

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.
..... Click the link for more information. 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

parabola

pa·rab·o·la

parabola

pa•rab•o•la

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parabola

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Parabola

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PARABOLA

parabola

Words related to parabola

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

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