Parabola

parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. As a plane curve, it may be defined as the path (locus) of a point moving so that its distance from a fixed line (the directrix) is equal to its distance from a fixed point (the focus).

The vertex of the parabola is the point on the curve that is closest to the directrix; it is equidistant from the directrix and the focus. The vertex and the focus determine a line, perpendicular to the directrix, that is the axis of the parabola. The line through the focus parallel to the directrix is the latus rectum (straight side). The parabola is symmetric about its axis, moving farther from the axis as the curve recedes in the direction away from its vertex. Rotation of a parabola about its axis forms a paraboloid.

The parabola is the path, neglecting air resistance and rotational effects, of a projectile thrown outward into the air. The parabolic shape also is seen in certain bridges, either as arches, or in the case of a suspension bridge, as the shape assumed by the main cable, if one assumes the weight of the vertical cables is small compared to the weight of the roadway they support.

For a parabola whose axis is the x-axis and with vertex at the origin, the equation is y²= 2px, in which p is the distance between the directrix and the focus.