Hyperbola or in plural hyperbolae is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the four kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola, the ellipse, and the circle; the circle is a special case of the ellipse). If the plane intersects both halves of the double cone but does not pass through the apex of the cones then the conic is a hyperbola.