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Hyperbola

In mathematics, a hyperbola (/haɪˈpɜːrbələ/ hy-PUR-bə-lə) 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…

History & Applications

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Overview

Etymology and history

Definitions

In Cartesian coordinates

In polar coordinates

Parametric equations

Hyperbolic functions

Properties

Arc length

Derived curves

Elliptic coordinates

Conic section analysis of the hyperbolic appearance of circles

Applications

Hyperbolas as plane sections of quadrics

Other related topics

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Map overview Semantic statistics

Hyperbola

Nodes176
Edges175
Triples194
Avg. degree1.99
Density0.011364
Components1

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Hyperbola

Top relations

related to Angle trisection · 21
Hyperbola → Angle POB, AOB, Apollonius, As, As OA, BP, Construct, Given, Let, Next, OAP, OB, OP, OPB, OPP, Perga, POB, PP, Segment AP, Therefore
related to history · 10
Hyperbola → Apollonius, BC, Conics, English, Greek, Hyperbolae, Menaechmus, Perga, Pythagorean, The
is a · 9
Hyperbola → affine image of the hyperbola y, affine image of the unit hyperbola with equation x 2, affine version of the 3-point-degeneration of Pascal's theorem.Area of the grey parallelogramThe area of the grey parallelogram M A P B, affine version of the 4-point-degeneration of Pascal's theorem, affine version of the 4-point-degeneration of Pascal's theorem.Tangent, basis for solving multilateration problems, essential tool for the determination of the orthoptic of a hyperbola, Klein four-group.The rectangular hyperbolas xy, set of points
related to As plane section of a cone · 9
Hyperbola → AB, Dandelin, In, It, Let, PA, PB, The, Therefore
related to External links · 9
Hyperbola → Apollonius' Derivation, ConvergenceMathematische Oeffeningen, EMS Press, Encyclopedia, Eric, Frans, Mathematics, MathWorld, Schooten
related to Reflection property · 9
Hyperbola → But, From, Hence, In, Let, Line, QL, The, This
related to Hyperbolic functions · 8
Hyperbola → From, In, Just, Let, Other, Solving, The, Then
related to Parametric equations · 8
Hyperbola → As, Here, One, Replace, The, This, Through, With
related to Path followed by a particle · 7
Hyperbola → Coulomb, If, In, Kepler, Rutherford, The, This
related to Pin and string construction · 7
Hyperbola → AB, Choose, PB, Point, Rotating, Take, The

Important terminology Word statistics

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Important terminology

displaystyle point equation center frac one two circle points right left line tfrac tangent see vec called plane asymptotes eccentricity

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hyperbolais aset of points0.90text
Hyperbolais aaffine image of the unit hyperbola with equation x 20.90text
Hyperbolais aaffine version of the 3-point-degeneration of Pascal's theorem.Area of the grey parallelogramThe area of the grey parallelogram M A P B0.90text
Hyperbolais aaffine version of the 4-point-degeneration of Pascal's theorem.Tangent0.90text
Hyperbolais aaffine version of the 4-point-degeneration of Pascal's theorem0.90text
Hyperbolais aessential tool for the determination of the orthoptic of a hyperbola0.90text
Hyperbolais aaffine image of the hyperbola y0.90text
Hyperbolais aKlein four-group.The rectangular hyperbolas xy0.90text
Hyperbolais abasis for solving multilateration problems0.90text
the reciprocal relationship x yinstance ofor as the solution of certain bivariate quadratic equations0.80text
eccentricityinstance ofthe asymptotes are the two coordinate axes.Hyperbolas share many of the ellipses' analytical properties0.80text
focusinstance ofthe asymptotes are the two coordinate axes.Hyperbolas share many of the ellipses' analytical properties0.80text

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