Definitions for hyperbola
haɪˈpɜr bə ləhy·per·bo·la

Princeton's WordNetRate this definition:0.0 / 0 votes

1. hyperbolanoun

   an open curve formed by a plane that cuts the base of a right circular cone

WiktionaryRate this definition:0.0 / 0 votes

1. hyperbolanoun

   A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone.

Samuel Johnson's DictionaryRate this definition:0.0 / 0 votes

1. HYPERBOLAnoun

   In geometry, a section of a cone made by a plane, so that the axis of the section inclines to the opposite leg of the cone, which in the parabola is parallel to it, and in the ellipsis intersects it. The axis of the hyperbolical section will meet also with the opposite side of the cone, when produced above the vertex. John Harris

   Etymology: hyperbole, Fr. ὕπεϱ and βάλλω.

   Had the velocities of the several planets been greater or less than they are, or had their distances from the sun, or the quantity of the sun’s matter, and consequently his attractive power been greater or less than they are now, with the same velocities, they would not have revolved in concentrick circles, but have moved in hyperbola’s very eccentrick. Richard Bentley, Serm.

WikipediaRate this definition:0.0 / 0 votes

1. Hyperbola

   In mathematics, a hyperbola ( (listen); pl. hyperbolas or hyperbolae (listen); adj. hyperbolic (listen)) 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. Hyperbolas arise in many ways: as the curve representing the reciprocal function y ( x ) = 1 / x {\displaystyle y(x)=1/x} in the Cartesian plane, 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 (or celestial object) exceeding the escape velocity of the nearest planet or other gravitational body, as the scattering trajectory of a subatomic particle (acted on by repulsive instead of attractive forces but the principle is the same), in radio navigation, when the difference between distances to two points, but not the distances themselves, can be determined,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 y ( x ) = 1 / x {\displaystyle y(x)=1/x} 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 proposed for use in both relativity and quantum mechanics which is not Euclidean).

ChatGPTRate this definition:0.0 / 0 votes

1. hyperbola

   A hyperbola 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. It consists of two symmetrical curves, each approaching a different fixed point as they extend to infinity. A hyperbola is also the set of all points in a plane where the difference of the distances to two fixed points (foci) is constant. It's an open curve formed of two disconnected sections or branches.

Webster DictionaryRate this definition:0.0 / 0 votes

1. Hyperbolanoun

   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

2. Etymology: [Gr. "yperbolh`, prop., an overshooting, excess, i. e., of the angle which the cutting plane makes with the base. See Hyperbole.]

WikidataRate this definition:0.0 / 0 votes

1. Hyperbola

   In mathematics a hyperbola 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 cone. The other conic sections are the parabola, the ellipse, and the circle. Which conic section is formed depends on the angle the plane makes with the axis of the cone, compared with the angle a straight line on the surface of the cone makes with the axis of the cone. If the angle between the plane and the axis is less than the angle between the line on the cone and the axis, or if the plane is parallel to the axis, then the plane intersects both halves of the double cone and the conic is a hyperbola. Hyperbolas arise in practice 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, 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, as the scattering trajectory of a subatomic particle, and so on.

Chambers 20th Century DictionaryRate this definition:0.0 / 0 votes

1. Hyperbola

   hī-per′bo-la, n. (geom.) one of the conic sections or curves formed when the intersecting plane makes a greater angle with the base than the side of the cone makes.—adjs. Hyperbol′ic, -al.—adv. Hyperbol′ically.—adjs. Hyperbol′iform; Hyper′boloid. [L.,—Gr. hyperbolē, from hyperballein—hyper, beyond, ballein, to throw.]

Dictionary of Nautical TermsRate this definition:0.0 / 0 votes

1. hyperbola

   One of the conic sections formed by cutting a cone by a plane which is so inclined to the axis, that when produced it cuts also the opposite cone, or the cone which is the continuation of the former, on the opposite side of the vertex.

Matched Categories

1. • Conic Section

How to pronounce hyperbola?

1. Alex

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How to say hyperbola in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of hyperbola in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of hyperbola in Pythagorean Numerology is: 3

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=hyperbola
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Hyperbola
3. ^ Samuel Johnson's Dictionary
   https://johnsonsdictionaryonline.com/views/search.php?term=hyperbola
4. ^ Wikipedia
   https://en.wikipedia.org/wiki/Hyperbola
5. ^ ChatGPT
   https://chat.openai.com
6. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/hyperbola
7. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=hyperbola
8. ^ Chambers 20th Century Dictionary
   https://www.gutenberg.org/files/37683/37683-h/37683-h.htm#:~:text=hyperbola
9. ^ Dictionary of Nautical Terms
   https://www.gutenberg.org/cache/epub/26000/pg26000-images.html#:~:text=hyperbola