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The image shaws a double cone in which a geometrical plane haes sliced aff pairts o the tap an bottom hauf; the boondary curve o the slice on the cone is the hyperbola. A double cone consists o twa cones stacked pynt-tae-pynt an sharin the same axis o rotation; it mey be generatit bi rotatin a line aboot an axis that passes through a pynt o the line.
A hyperbola is an open curve wi twa branches, the intersection o a plane wi baith halves o a double cone. The plane daes nae hae tae be parallel tae the axis o the cone; the hyperbola will be symmetrical in ony case.

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 ilk 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.