The parabola ( from the Greek Ï Î Ï Î Î Î Î '' Î ) is a type of regular curve , the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface . In mathematics , the parabola ( ; plural parabolae or parabolas , from the Greek Ï Î Ï Î Î Î Î '' Î ) is a conic section , the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface .