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 &math.y; = &math.a;&math.x;2 + &math.b;&math.x; + &math.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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