parabola

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 section 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.

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parabola

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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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

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parabola [pə′rab·ə·lə]

(mathematics)

The plane curve given by an equation of the formy=ax²+bx+c.