In mathematics, an ellipse (from Greek ἔλλειψις elleipsis, a
"falling short") is a plane curve that results from the
intersection of a cone by a plane in a way that produces a
closed curve. Circles are special cases of ellipses, obtained
when the cutting plane is orthogonal to the cone's axis. An
ellipse is also the locus of all points of the plane whose
distances to two fixed points add to the same constant. The name
ἔλλειψις was given by Apollonius of Perga in his Conics,
emphasizing the connection of the curve with "application of
areas". Ellipses are closed curves and are the bounded case of
the conic sections, the curves that result from the intersection
of a circular cone and a plane that does not pass through its
apex; the other two (open and unbounded) cases are parabolas and
hyperbolas. Ellipses arise from the intersection of a right
circular cylinder with a plane that is not parallel to the
cylinder's main axis of symmetry. Ellipses also arise as images
of a circle under parallel projection and the