n. a closed geometric figure shaped like an elongated circle and symmetric about two axes of different lengths (the major and minor axes); the conic section with eccentricity less than 1. In the figure below the axes of symmetry are both shown, and the eccentricity is the ratio PF/PX, where F is a focus and X the foot of the perpendicular from the variable point P to the directrix DE.An ellipse is formed by the intersection of a bounded nappe of a right circular cone with a plane that does not cut its base; that is, it is the projection of a circle onto another non-parallel plane, and it is the locus of points for which the sum of the distances from the two foci is constant. The canonical equation of an ellipse is when the ellipse is symmetrical about the origin as shown, and intersects the axes at the points (±a, 0) and (0, ±b); its parametric equations are It has its foci at (±ae, 0), where e is the eccentricity, and The area is then π ab, but there is no general closed form for the perimeter without using elliptic integrals.