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• Hyperbola abstract "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 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.Hyperbolas arise in many ways: as the curve representing the function in the Cartesian plane, as the appearance of a circle viewed from within it, as the path followed by the shadow of the tip of a sundial, as the shape of an open orbit (as distinct from a closed elliptical orbit), such as the orbit of a spacecraft during a gravity assisted swing-by of a planet or more generally any spacecraft exceeding the escape velocity of the nearest planet, as the path of a single-apparition comet (one travelling too fast to ever return to the solar system), as the scattering trajectory of a subatomic particle (acted on by repulsive instead of attractive forces but the principle is the same), and so on.Each branch of the hyperbola has two arms which become straighter (lower curvature) further out from the center of the hyperbola. Diagonally opposite arms, one from each branch, tend in the limit to a common line, called the asymptote of those two arms. So there are two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch. In the case of the curve the asymptotes are the two coordinate axes.Hyperbolas share many of the ellipses' analytical properties such as eccentricity, focus, and directrix. Typically the correspondence can be made with nothing more than a change of sign in some term. Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids (saddle surfaces), hyperboloids ("wastebaskets"), hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry used in both relativity and quantum mechanics which is not Euclidean).".
• Hyperbola thumbnail Hyperbola_(PSF).svg?width=300.
• Hyperbola wikiPageExternalLink 1.
• Hyperbola wikiPageExternalLink ?pa=content&sa=viewDocument&nodeId=196&bodyId=204.
• Hyperbola wikiPageID "14052".
• Hyperbola wikiPageRevisionID "605306481".
• Hyperbola hasPhotoCollection Hyperbola.
• Hyperbola id "3584".
• Hyperbola id "5996".
• Hyperbola id "6241".
• Hyperbola id "p/h048230".
• Hyperbola title "Conic section".
• Hyperbola title "Conjugate hyperbola".
• Hyperbola title "Hyperbola".
• Hyperbola title "Unit hyperbola".
• Hyperbola subject Category:Analytic_geometry.
• Hyperbola subject Category:Conic_sections.
• Hyperbola subject Category:Curves.
• Hyperbola comment "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 four kinds of conic section, formed by the intersection of a plane and a double cone.".
• Hyperbola label "Hiperbola (matematyka)".
• Hyperbola label "Hipérbola".
• Hyperbola label "Hipérbole".
• Hyperbola label "Hyperbel (Mathematik)".
• Hyperbola label "Hyperbola".
• Hyperbola label "Hyperbole (mathématiques)".
• Hyperbola label "Hyperbool (meetkunde)".
• Hyperbola label "Iperbole (geometria)".
• Hyperbola label "Гипербола (математика)".
• Hyperbola label "قطع زائد".
• Hyperbola label "双曲線".
• Hyperbola label "双曲线".
• Hyperbola sameAs Hyperbola.
• Hyperbola sameAs Hyperbel_(Mathematik).
• Hyperbola sameAs Υπερβολή_(γεωμετρία).
• Hyperbola sameAs Hipérbola.
• Hyperbola sameAs Hiperbola.
• Hyperbola sameAs Hyperbole_(mathématiques).
• Hyperbola sameAs Iperbole_(geometria).
• Hyperbola sameAs 双曲線.
• Hyperbola sameAs 쌍곡선.
• Hyperbola sameAs Hyperbool_(meetkunde).
• Hyperbola sameAs Hiperbola_(matematyka).
• Hyperbola sameAs Hipérbole.
• Hyperbola sameAs m.03n7n.
• Hyperbola sameAs Q165301.
• Hyperbola sameAs Q165301.
• Hyperbola wasDerivedFrom Hyperbola?oldid=605306481.
• Hyperbola depiction Hyperbola_(PSF).svg.
• Hyperbola isPrimaryTopicOf Hyperbola.