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Plane curve: conic section
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
Hyperbola
Topics referred to by the same term
A hyperbola is a type of smooth curve lying in a plane. Hyperbola may also refer to: Hesperorhipis hyperbola, a species of metallic wood-boring beetles
Hyperbola_(disambiguation)
Chinese space launch company
[citation needed] By 2019, i-Space had successfully launched the Hyperbola-1S and Hyperbola-1Z single-stage solid-propellant test rockets into space on suborbital
I-Space_(Chinese_company)
Geometric figure
In geometry, the unit hyperbola is the set of points ( x , y ) {\displaystyle (x,y)} in the Cartesian plane that satisfy the implicit equation x 2 − y
Unit_hyperbola
Linux distribution
Hyperbola GNU/Linux-libre is a Linux distribution for the i686 and x86-64 architectures, including the GNU operating system components and the Linux-libre
Hyperbola_GNU/Linux-libre
Curve from a cone intersecting a plane
surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse
Conic_section
Chinese satellite launch vehicle
The Hyperbola-1 (aka Shuangquxian-1, SQX-1) (Chinese: 双曲线一号) rocket is 20.8 m (68 ft) tall, 1.4 m (4 ft 7 in) in diameter and weighs 31 t (34 tons). It
Hyperbola-1
Term in geometry; longest and shortest semidiameters of an ellipse
the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Characteristic of conic sections
between 0 and 1. The eccentricity of a parabola is 1. The eccentricity of a hyperbola is greater than 1. The eccentricity of a pair of lines is ∞ . {\displaystyle
Eccentricity_(mathematics)
Symmetric figure defined by a hyperbola
conjugate hyperbola to a given hyperbola shares the same asymptotes but lies in the opposite two sectors of the plane compared to the original hyperbola. A hyperbola
Conjugate_hyperbola
Hyperbolic analogues of trigonometric functions
analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle
Hyperbolic_functions
Conic sections with the same foci
ellipses and hyperbolas have two foci, there are confocal ellipses, confocal hyperbolas and confocal mixtures of ellipses and hyperbolas. In the mixture
Confocal_conic_sections
Belgian Jesuit and mathematician (1584–1667)
and mathematician. He is remembered for his work on quadrature of the hyperbola. He is also known as Gregorio a San Vincente. Grégoire gave the "clearest
Grégoire_de_Saint-Vincent
Unique curve associated with every triangle
In geometry, the Feuerbach hyperbola is a rectangular hyperbola passing through important triangle centers such as the incenter, orthocenter, Gergonne
Feuerbach_hyperbola
Conic curves associated with a triangle
associated with the reference triangle. One of them is a hyperbola, called the Kiepert hyperbola and the other is a parabola, called the Kiepert parabola
Kiepert_conics
Plane algebraic curve
circle inversion transformation to a hyperbola, where the center of inversion is the midpoint of the hyperbola's foci. It can also be drawn mechanically
Lemniscate_of_Bernoulli
Unbounded quadric surface
called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained
Hyperboloid
Perpendicular diameters of a circle or hyperbolic-orthogonal diameters of a hyperbola
conjugate hyperbola: "If Q be any point on a hyperbola and CE be drawn from the centre parallel to the tangent at Q to meet the conjugate hyperbola in E,
Conjugate_diameters
All points for which two tangents of a curve intersect at 90° angles
{\displaystyle x^{2}+y^{2}=a^{2}+b^{2}} (see below), The orthoptic of a hyperbola x 2 a 2 − y 2 b 2 = 1 , a > b {\displaystyle {\tfrac {x^{2}}{a^{2}}}-{\tfrac
Orthoptic_(geometry)
Mathematical functions
{arsinh} x)=x.} Hyperbolic angle measure is the length of an arc of a unit hyperbola x 2 − y 2 = 1 {\displaystyle x^{2}-y^{2}=1} as measured in the Lorentzian
Inverse_hyperbolic_functions
Region of the Cartesian plane bounded by a hyperbola and two radii
bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a) and (b, 1/b) on the rectangular hyperbola xy = 1, or the
Hyperbolic_sector
Reals with an extra square root of +1 adjoined
z\rVert ^{2}=a^{2}\right\}} is a hyperbola for every nonzero a in R . {\displaystyle \mathbb {R} .} The hyperbola consists of a right and left branch
Split-complex_number
Mathematical tool for summing arithmetic functions
In number theory, the Dirichlet hyperbola method is a technique to evaluate the sum F ( n ) = ∑ k = 1 n f ( k ) {\displaystyle F(n)=\sum _{k=1}^{n}f(k)}
Dirichlet_hyperbola_method
Curve on the sphere analogous to an ellipse or hyperbola
It is the spherical analog of a conic section (ellipse, parabola, or hyperbola) in the plane, and as in the planar case, a spherical conic can be defined
Spherical_conic
Hyperbola constructed from a given triangle and point
In Euclidean geometry with triangle △ABC, the nine-point hyperbola is an instance of the nine-point conic described by American mathematician Maxime Bôcher
Nine-point_hyperbola
Geometric point from which certain types of curves are constructed
sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian
Focus_(geometry)
Geometric inversion of a torus, cylinder or double cone
directrices are focal conics and consists either of an ellipse and a hyperbola or of two parabolas. In the first case one defines the cyclide as elliptic
Dupin_cyclide
Relationship between two lines that meet at a right angle
a hyperbola is perpendicular to the conjugate axis and to each directrix. The product of the perpendicular distances from a point P on a hyperbola or
Perpendicular
Quadric surface that looks like a deformed sphere
runs from S1 to P behind the upper part of the hyperbola (see diagram) and is free to slide on the hyperbola. The part of the string from P to F2 runs and
Ellipsoid
Topics referred to by the same term
the free dictionary. Hyperbolic may refer to: of or pertaining to a hyperbola, a type of smooth curve lying in a plane in mathematics Hyperbolic geometry
Hyperbolic
Coordinate system for the Schwarzschild geometry
cone will eventually hit the black hole singularity, which appears as a hyperbola bounded by the two black hole horizons), and any event inside the white
Kruskal–Szekeres_coordinates
Conic plane curve associated with a given triangle
triangle circle (respectively, ellipse, hyperbola, parabola) is used to denote a circle (respectively, ellipse, hyperbola, parabola) associated with the reference
Triangle_conic
Linear map that preserves areas
{constant} \}} is a hyperbola, if u = ax and v = y/a, then uv = xy and the points of the image of the squeeze mapping are on the same hyperbola as (x,y) is.
Squeeze_mapping
Argument of the hyperbolic functions
an area against hyperbola xy = 1, and they both are preserved by squeeze mappings since those mappings preserve area. The hyperbola xy = 1 is rectangular
Hyperbolic_angle
Problem in celestial mechanics
on the right branch of the hyperbola depending on the sign of A {\displaystyle A} . The semi-major axis of this hyperbola is | A | {\displaystyle |A|}
Lambert's_problem
Species of beetle
hyperbola californica Knull, 1947 Hesperorhipis hyperbola hyperbola Knull, 1938 "Hesperorhipis hyperbola Species Information". BugGuide.net. Iowa State
Hesperorhipis_hyperbola
Geometric curve associated with a quadrangle
better-known nine-point circle is an instance of Bôcher's conic. The nine-point hyperbola is another instance. Bôcher used the four points of the complete quadrangle
Nine-point_conic
Development of the mathematical function
the result of a search for an expression of area against a rectangular hyperbola, and required the assimilation of a new function into standard mathematics
History_of_logarithms
2nd-degree plane curve which is reducible
the limit case a = 1 , b = 0 {\displaystyle a=1,b=0} in the pencil of hyperbolas of equations a ( x 2 − y 2 ) − b = 0. {\displaystyle a(x^{2}-y^{2})-b=0
Degenerate_conic
Species of moth
juglandis (J.E. Smith, 1797) Sphinx instibilis Martyn, 1797 Cressonia hyperbola Slosson, 1890 Cressonia robinsonii Butler, 1876 Smerinthus pallens Strecker
Amorpha_juglandis
Mathematical proof technique
points on hyperbolas in the first quadrant. The same process of finding smaller roots is used instead to find lower lattice points on a hyperbola while remaining
Vieta_jumping
On reflection in a spherical mirror
the later ones. Ibn al-Haytham's solution is of the second type, using hyperbola, through which he develops a neusis construction. In his 1881 survey of
Alhazen's_problem
Polynomial function of degree two
describe a conic section (a circle or other ellipse, a parabola, or a hyperbola) in the x {\displaystyle x} – y {\displaystyle y} plane. A quadratic
Quadratic_function
Relation of space and time in relativity theory
In geometry, given a pair of conjugate hyperbolas, two conjugate diameters are hyperbolically orthogonal. This relationship of diameters was described
Hyperbolic_orthogonality
Amount by which an orbit deviates from a perfect circle
a parabolic (escape orbit or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every
Orbital_eccentricity
Belgian mathematician (1618 to 1667)
contributed to the understanding of logarithms, particularly as areas under a hyperbola. Alphonse de Sarasa was born in 1618, in Nieuwpoort in Flanders. In 1632
Alphonse_Antonio_de_Sarasa
Volunteer-run lightning detection network
arrival times of the signals. Figuratively speaking, the server draws a hyperbola line around two of the receivers, which can be calculated from the propagation
Blitzortung
Circle formed by all 90° crossings of tangents of an ellipse or hyperbola
In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermat–Apollonius circle) is a circle consisting of all
Director_circle
Index of articles associated with the same name
of two ellipses, two hyperbolas, or an ellipse and a hyperbola which share both foci with each other. If an ellipse and a hyperbola are confocal, they are
Confocal
Family of curves of the form r^n = a^n cos(nθ)
Many well known curves are sinusoidal spirals including: Rectangular hyperbola (n = −2) Line (n = −1) Parabola (n = −1/2) Tschirnhausen cubic (n = −1/3)
Sinusoidal_spiral
Ancient Greek geometer and astronomer (c. 240–190 BC)
analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes
Apollonius_of_Perga
Pairs of conic sections in geometry
and a hyperbola, where the hyperbola is contained in a plane, which is orthogonal to the plane containing the ellipse. The vertices of the hyperbola are
Focal_conics
4th-century BC Greek mathematician
then-long-standing problem of doubling the cube using the parabola and hyperbola. Menaechmus is remembered by mathematicians for his discovery of the conic
Menaechmus
Geometry problem about finding touching circles
16th century, Adriaan van Roomen solved the problem using intersecting hyperbolas, but this solution uses methods not limited to straightedge and compass
Problem_of_Apollonius
Representation of a curve by a function of a parameter
constants describing the number of lobes of the figure. An east-west opening hyperbola can be represented parametrically by x = a sec t + h y = b tan t +
Parametric_equation
Partially-reusable medium-lift launch vehicle by SpaceX
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Falcon_9
Circle constructed from a triangle
rectangular hyperbolas that pass through the vertices of a triangle lies on its nine-point circle. Examples include the well-known rectangular hyperbolas of Keipert
Nine-point_circle
1962 concept for a reusable, sea-launched rocket
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Sea_Dragon_(rocket)
On sets of points with integer distances
also lie on one of d ( B , C ) + 1 {\displaystyle d(B,C)+1} hyperbolas or degenerate hyperbolas defined by equations of the form | d ( B , X ) − d ( C ,
Erdős–Anning_theorem
Point on a line segment which is equidistant from both endpoints
ellipse. The midpoint of a segment connecting a hyperbola's vertices is the center of the hyperbola. The perpendicular bisector of a side of a triangle
Midpoint
Concept in astrodynamics
a hyperbolic trajectory or hyperbolic orbit (from Newtonian theory: hyperbola shape) is the trajectory of any object around a central body with enough
Hyperbolic_trajectory
Principle in geometry and linear algebra
or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular
Principal_axis_theorem
Partially-reusable heavy-lift launch vehicle by Relativity Space
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Terran_R
Two-dimensional shape
section of a hyperbola that is tangent to the two sides adjacent to the corner and asymptotic to the sides adjacent to these. The hyperbola that forms each
Smoothed_octagon
point of rotational symmetries. Similarly the centre of an ellipse or a hyperbola is where the axes intersect. Several special points of a triangle are
Centre_(geometry)
Point pair associated with plane triangles
hyperbola and it is called the Kiepert hyperbola in honor of Ludwig Kiepert (1846–1934), the mathematician who discovered this result. This hyperbola
Napoleon_points
Algebraic structure in linear algebra
A hyperbola, given by the equation x ⋅ y = 1. {\displaystyle x\cdot y=1.} The coordinate ring of functions on this hyperbola is given by R [ x , y ] /
Vector_space
January 2024. "Releases". HyperWiki. Hyperbola Project. Retrieved 29 March 2022. Larabel, Michael. "FSF-Approved Hyperbola GNU/Linux Switching Out The Linux
Comparison of Linux distributions
Comparison_of_Linux_distributions
Three-dimensional orthogonal coordinate system
elliptic cylindrical coordinates. The yellow sheet is the prism of a half-hyperbola corresponding to ν=-45°, whereas the red tube is an elliptical prism corresponding
Elliptic cylindrical coordinates
Elliptic_cylindrical_coordinates
Rocket-powered aircraft and spaceplane operated by the US Air Force and NASA
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
North_American_X-15
Curve created by a geometric operation
a^{2}\left(u^{2}-v^{2}\right)=1,} the equation of a hyperbola; since inversion is a birational transformation and the hyperbola is a rational curve, this shows the lemniscate
Inverse_curve
2.71828...; base of natural logarithms
The five colored regions are of equal area, and define units of hyperbolic angle along the hyperbola x y = 1. {\displaystyle xy=1.}
E_(mathematical_constant)
Motion of an object with constant proper acceleration in special relativity
the equation describing the path of the object through spacetime is a hyperbola. It can be visualized when graphed on a Minkowski diagram, whose position
Hyperbolic motion (relativity)
Hyperbolic_motion_(relativity)
Chinese launch site
first successful Chinese private orbital launch from Jiuquan using the Hyperbola-1 rocket.[citation needed] The launch site includes two launch complexes
Jiuquan Satellite Launch Center
Jiuquan_Satellite_Launch_Center
Conic section that passes through the vertices of a triangle or is tangent to its sides
or 2 points according as the circumconic is an ellipse, parabola, or hyperbola. In barycentric coordinates, the general inconic is tangent to the three
Circumconic_and_inconic
Chinese medium-lift reusable carrier rocket
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Long_March_12B
Single-stage-to-orbit spaceplane
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Skylon_(spacecraft)
Partially reusable launch system and space plane
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Space_Shuttle
Partially-reusable medium-lift launch vehicle
methane-fueled medium lift-off systems) LandSpace Zhuque-3 Long March 12A i-Space Hyperbola-3 Soyuz-7 "Rocket Lab targets $50 million launch price for Neutron rocket
Rocket_Lab_Neutron
Partly reusable Orbital launch vehicle by LandSpace of China
(Reusable methane-fueled medium lift-off systems) Long March 12A i-Space Hyperbola-3 Rocket Lab Neutron Soyuz-7 "Re: Maiden - Zhuque-3 (Y1) - Jiuquan - December
Zhuque-3
Geometric mean and hyperbolic angle as coordinates in quadrant I
left-right shift corresponds to a squeeze mapping applied to Q. Since hyperbolas in Q correspond to lines parallel to the boundary of HP, they are horocycles
Hyperbolic_coordinates
Proposed age of religious and philosophical change from the 8th to 3rd centuries BCE
Ostrovsky, Max (2006). The Hyperbola of the World Order, (Lanham: University Press of America) Ostrovsky, Max (2006). The Hyperbola of the World Order, (Lanham:
Axial_Age
Three-dimensional solid
a right section of a cylinder is a conic section (parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic
Cylinder
Collinearity of the midpoints of parallel chords in a conic
segment for the midpoints is called the diameter. For a circle, ellipse or hyperbola the diameter goes through its center. For a parabola the diameter is always
Midpoint_theorem_(conics)
Study of geometry using a coordinate system
equation represents a hyperbola; if we also have A + C = 0 {\displaystyle A+C=0} , the equation represents a rectangular hyperbola. A quadric, or quadric
Analytic_geometry
Intersection of triangle altitudes
Weisstein, Eric W. "Jerabek Hyperbola." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/JerabekHyperbola.html Berele & Goldman 2001
Orthocenter
Laws in physics about force and motion
conic sections, that is, ellipses (including circles), parabolas, or hyperbolas. The eccentricity of the orbit, and thus the type of conic section, is
Newton's_laws_of_motion
One of the physical forms of elemental oxygen
(under development) Galactic Energy: Pallas-1 (under development) i-Space: Hyperbola-3 (under development) LandSpace: Zhuque-2E, Zhuque-3 Orienspace: Gravity-2
Liquid_oxygen
Property of two varying quantities with a constant ratio
varying inversely on the Cartesian coordinate plane is a rectangular hyperbola. The product of the x and y values of each point on the curve equals the
Proportionality_(mathematics)
Various meanings of the terms
features relativity of simultaneity. In geometry, given a pair of conjugate hyperbolas, two conjugate diameters are hyperbolically orthogonal. This relationship
Orthogonality
Soviet launch vehicle
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Energia_(rocket)
Plane curve constructed from two other curves and a fixed point
x^{2}-m^{2}y^{2}=bx+cy.} This is a hyperbola passing through the origin. So the cissoid of two non-parallel lines is a hyperbola containing the pole. A similar
Cissoid
Logarithm to the base of the mathematical constant e
Antonio de Sarasa before 1649. Their work involved quadrature of the hyperbola with equation xy = 1, by determination of the area of hyperbolic sectors
Natural_logarithm
Lines which intersect at a single point
ellipse. In a hyperbola the following are concurrent: (1) a circle passing through the hyperbola's foci and centered at the hyperbola's center; (2) either
Concurrent_lines
Dutch statesman (1625–1672)
well as the contemporary Claude Mydorge. Johan de Witt describes the hyperbola with a rotating line and a sliding angle, and a parabola by means of a
Johan_de_Witt
Chinese commercial medium-lift rocket
Space Nova Vulcan (engines) First stage Amur (Soyuz-7) Eclipse Gravity-2 Hyperbola-3 Long March 10A 10B 12A 12B Maia Miura 5 Nebula 1 2 Pallas 1 2 Neutron
Long_March_10B
Mathematical model combining space and time
diagram, which are termed invariant hyperbolae. In Fig. 2-7a, each magenta hyperbola connects all events having some fixed spacelike separation from the origin
Spacetime
Quartic plane curve
r^{-1}} is the polar equation of a hyperbola with eccentricity equal to 2, a curve that is a trisectrix. (See Hyperbola - angle trisection.) Xah Lee. "Trisectrix"
Limaçon_trisectrix
Limit of the tangent line at a point that tends to infinity
that have one or two horizontal asymptotes include x ↦ 1/x (that has an hyperbola as it graph), the Gaussian function x ↦ exp ( − x 2 ) , {\displaystyle
Asymptote
Mathematical framework for investment risk
hyperbolic boundary is the capital allocation line (CAL). The vertex of the hyperbola represents the Global Minimum Variance Portfolio (GMVP), which is the
Modern_portfolio_theory
HYPERBOLA
HYPERBOLA
HYPERBOLA
HYPERBOLA
Male
Slovene
Short form of Slovene Ignacij, possibly IGNAC means "unknowing."
Boy/Male
Hindu
Lord of Love
Girl/Female
Australian, British, English
Cool; Pleasent; Love
Boy/Male
Arabic
Gift
Girl/Female
Shakespearean
Antony and Cleopatra'. Lady attending on Cleopatra.
Boy/Male
Biblical
Who demands his death.
Male
Dutch
, Christ-bearer.
Girl/Female
Muslim
Beloved, Goddess of Love
Boy/Male
English
or John.
Boy/Male
Muslim
The bestower
HYPERBOLA
HYPERBOLA
HYPERBOLA
HYPERBOLA
HYPERBOLA
adv.
In the form of an hyperbola.
n.
The ratio of the distance between the center and the focus of an ellipse or hyperbola to its semi-transverse axis.
a.
Having the form, or nearly the form, of an hyperbola.
n.
One of the portions of a curve that extends outwards to an indefinitely great distance; as, the branches of an hyperbola.
n.
A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.
n.
A certain conic section supposed to be drawn in the tangent plane to any surface, and used to determine the accidents of curvature of the surface at the point of contact. The curve is similar to the intersection of the surface with a parallel to the tangent plane and indefinitely near it. It is an ellipse when the curvature is synclastic, and an hyperbola when the curvature is anticlastic.
n.
A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.
a.
Having some property that belongs to an hyperboloid or hyperbola.
a.
Belonging to the hyperbola; having the nature of the hyperbola.
n.
A curve in the form of the figure 8, with both parts symmetrical, generated by the point in which a tangent to an equilateral hyperbola meets the perpendicular on it drawn from the center.
n.
Specifically (Conic Sections), in the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.