Parabola

The parabola (from the Greek: παραβολή) is a conic section generated by the intersection of a cone and a plane tangent to the cone or parallel to some plane tangent to the cone. If the plane is itself tangent to the cone, one would obtain a degenerate parabola, a line. A parabola can also be defined as locus of points which are equidistant from a given point (the focus) and a given line (the directrix).

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Algebraically, a parabola is a curve in the Cartesian plane defined by

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an irreducible equation of the form

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:A x^2 + B xy + C y^2 + D x + E y + F = 0

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such that B^2 = 4 AC, where all of the coefficients are real, and where more than one solution, defining a pair of points (x, y) on the parabola, exists. That the equation is irreducible means it does not factor as a product of two not necessarily distinct linear factors

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Greek: The noun Greek refers to:...

Conic section: In mathematics, a conic section (or just conic) is a curved locus of points, formed by intersecting a cone with a plane. The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their properties....

Cone: A cone is a basic geometrical shape: see cone (solid). Several things have also been called "cones" on account of their shape:...