In mathematics, a hyperbola is a type o smuith curve, lyin in a plane, defined bi its geometric properties or bi equations for which it is the solution set. A hyperbola haes twa pieces, cried connectit components or branches, that are mirror images o each ither an resemble twa infinite bows. The hyperbola is ane o the fower kinds o conic section, furmed bi the intersection o a plane an a double cone. (The other conic sections are the parabola, the ellipse, an the circle; the circle is a special case o the ellipse). If the plane intersects baith halves o the double cone but daes nae pass through the apex o the cones then the conic is a hyperbola.