ellipsformade

Ellipsformade describes objects or outlines that have the form of an ellipse. In geometry, an ellipse is defined as the set of all points for which the sum of the distances to two fixed points, called foci, is constant. The ellipse has a major axis of length 2a and a minor axis of length 2b, with eccentricity e = sqrt(1 − b^2/a^2). The distance from the center to each focus is c, where c^2 = a^2 − b^2, and the foci lie on the major axis. If a = b, the ellipse becomes a circle.

Two fundamental properties are often noted: the sum of the distances from any point on the ellipse to the two foci equals 2a, and a ray emanating from one focus reflects off the ellipse to pass through the other focus (the reflective property), which explains the use of ellipses in optics and acoustics.

Ellipsformade shapes appear in various contexts. Many planetary orbits are well described as ellipses with the Sun at one focus; in design and architecture they yield elongated, rounded contours; and in sports, oval running tracks or courts may be described as ellipsiformed. In practice, real objects labeled ellipsformade are often approximations, influenced by perspective, projection, or manufacturing tolerances.

See also: ellipse, conic section, eccentricity, focal points.