# Parabola

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A conic section generated by a the intersection of a cone and a plane parallel to some plane tangent to the cone. (If the plane is itself a tangent plane, one obtains a degenerate parabola consisting simply of a line.) A parabola may also be considered to be the set of points such that the distances of each point from a given point (the focus) and a given straight line (the directrix) are equal.

In Cartesian coordinates a parabola has the equation y=a x2 + c, with respect to some suitable coordinates.

A parabola may also be characterized as a conic section with an eccentricity of 1. As a consequence of this, all parabolas are similar. A parabola can also be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction.

A parabola has a single axis of reflective symmetry, which passes through its focus and is perpendicular to its directrix. A parabola spun about this axis in three dimensions traces out a shape known as a paraboloid of revolution. If a mirror is constructed in the shape of a paraboloid and a light source is placed at its focus, the light will be reflected as a beam of rays parallel to the axis, and the same process works in reverse. Thus, the parabola finds applications in the construction of telescopes, spotlights, and LED housings. The same reflection principle is used in radio telescopes and parabolic microphones as well.