A parabola is a conic section generated by the intersection of a cone, and a plane tangent to either the cone or some plane tangent to the cone. If the plane is itself tagent to the cone, one would obtain a degenerate parabola, a line. In other words, a parabola is the locus of points which are equidistant from a given point (the focus) and a given line (the directrix).

In Cartesian coordinates, a parabola with an axis parallel to the y axis with vertex (h, k), focus (h, k + p), and directrix y = k - p has the equation

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. The point of intersection of this axis and the parabola is called the vertex. A parabola spun about this axis in three dimensions traces out a shape known as a paraboloid of revolution. See also parabolic reflector.

A particle in motion under the influence of a uniform gravitational field (for instance, a baseball flying through the air, neglecting air friction) follows a parabolic trajectory.

Table of contents
1 Equations (Cartesian):
2 Equations (Parametric):
3 External Links

Equations (Cartesian):

Equations (Parametric):

See also: Ellipse, Hyperbola, Paraboloid.

External Links