Parabola

Parabola, in mathematics, plane curve, one of the conic sections, formed by the intersection of a cone with a plane parallel to a straight line on the slanting surface of the cone. Each point of the curve is equidistant from a fixed point, called the focus, and a fixed straight line, known as the directrix. The parabola is symmetrical about a line passing through the focus and perpendicular to the directrix. For a parabola symmetric about the x-axis and with its vertex at the origin, the mathematical equation is y² = 2 px, in which p is the distance between the focus and the directrix.

A parabola is the curve that describes the trajectory of a projectile, such as a bullet or a ball, in the absence of air resistance. Because of air resistance the curves in which projectiles travel only approximate true parabolas. Parabolic mirrors are reflectors that have the shape of a parabola rotated about the parabola's axis of symmetry. Parabolic mirrors reflect rays of light in parallel lines from a light source at the mirror's focus. Such reflectors are used in car headlights and all other forms of searchlights. Parabolic mirrors also bring parallel rays of light to a focus without spherical aberration. This type of reflector is therefore valuable in astronomical telescopes. Parabolic reflectors are used also as antennas in radio astronomy and radar.