1) An ellipse is a plane curve such that the sum of the distances from two fixed points (the foci) is constant. 2) It can be defined as the intersection of a cone by a plane that is not parallel to the central axis and at an angle greater than the generator. 3) The standard equation of an ellipse centered at the origin is x2/a2 + y2/b2 = 1, where a and b are the semi-major and semi-minor axes.