Parabola

Parabola, two-dimensional curve that matches the path a tossed object such as a ball follows. Each point on the curve is equally distant from a fixed point, called the focus, and a fixed straight line, known as the directrix. The very tip of a parabola is called the vertex.

Parabolas are important in astronomy and physical science. An object in space follows a parabolic orbit as it swings around a central mass if the object has just barely enough momentum to escape from the gravity of the central mass forever. An asteroid that followed such a path around the Sun would fly off into interstellar space, never to return. Parabolic mirrors (reflectors that have the shape of a parabola) reflect rays of light in parallel lines from a light source located at the mirror's focus.

Any parabola is symmetrical about a line that passes through the focus and is perpendicular to the directrix, meaning that the half-parabolas on each side of the line are mirror images of one another. A parabola can be drawn on xy axes by graphing its equation. For a parabola with a horizontal directrix and a vertex at (h, k), the equation is (x – h)² = 2p(y – k), in which p is the distance between the focus and the directrix. Conversely, the equation of a parabola with a vertical directrix is (y – k)² = 2p(x – h).

Parabolas are one of the conic section curves formed by the intersection of a right circular cone and a plane. A parabola is formed when the plane is parallel to a straight line drawn on the slanting surface of the cone from the tip of the cone to its base.