In geometry , an ellipse is a plane curve which results from the intersection of a cone by a plane in a way that produces a closed curve . In geometry , an ellipse ( from Greek á 1\/4 '' Î '' Î '' Î Î Ï Î Ï 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 .