In mathematics, a parabola is a U-shaped curve that can be defined in different ways. One way to define it is as a curve where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix) /12%3A_Analytic_Geometry/12.03%3A_The_Parabola). Another way to define it is as the set of all points in a plane that are the same distance from the focus and the directrix/12%3A_Analytic_Geometry/12.03%3A_The_Parabola). The vertex of the parabola is the point on the curve that is closest to the directrix and equidistant from the focus and the directrix. The axis of the parabola is the line perpendicular to the directrix that passes through the vertex. The latus rectum is the line segment through the focus that is perpendicular to the axis and has endpoints on the parabola. The standard equation of a parabola depends on the orientation of its axis of symmetry and the location of its vertex. For example, the standard equation of a parabola with a vertex at the origin and an axis of symmetry parallel to the y-axis is y^2 = 4px, where p is the distance between the focus and the directrix/12%3A_Analytic_Geometry/12.03%3A_The_Parabola). Parabolas have many applications in physics, engineering, and other fields. For example, they can be used to model the paths of projectiles, the shapes of satellite dishes and radar receivers, and the cables of suspension bridges.