In mathematics , a hyperbola plural hyperbolas or 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 three kinds of conic section , formed by the intersection of a plane and a double cone. The other conic sections are the parabola and the ellipse. A circle is a special case of an 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.
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