|
Search over 100 encyclopedias and dictionaries: |
Research categories | Follow us on Twitter |
Research categories
View all topics in the newsView all reference sources at Encyclopedia.com |
|||
hyperbola
hyperbola , plane curve consisting of all points such that the difference between the distances from any point on the curve to two fixed points (foci) is the same for all points. It is the conic section formed by a plane cutting both nappes of the cone ; it thus has two parts, or branches. The center of a hyperbola is the point halfway between its foci. The principal axis is the straight line through the foci. The vertices are the intersection of this axis with the curve. The transverse axis is the line segment joining the two vertices. The latus rectum is the chord through either focus perpendicular to the principal axis. The asymptotes are lines, in the same plane, which the curve approaches as it approaches infinity. An equilateral, or rectangular, hyperbola is one whose asymptotes are perpendicular. A second hyperbola may be drawn whose asymptotes are identical with those of the given hyperbola and whose principal axis is a perpendicular line through the center; the two hyperbolas thus related are called conjugate. |
|
|
Cite this article
"hyperbola." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. "hyperbola." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1E1-hyperbola.html "hyperbola." The Columbia Encyclopedia, 6th ed.. 2011. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1E1-hyperbola.html |
|
hyperbola
hy·per·bo·la
/ hīˈpərbələ/
•
n.
(pl. -bo·las
or -bo·lae
/ -bəlē/
)
a symmetrical open curve formed by the intersection of a cone with a plane at a smaller angle with its axis than the side of the cone.
∎ Math.
the pair of such curves formed by the intersection of a plane with two equal cones on opposites of the same vertex.
hyperbola |
|
|
Cite this article
"hyperbola." The Oxford Pocket Dictionary of Current English. 2009. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. "hyperbola." The Oxford Pocket Dictionary of Current English. 2009. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O999-hyperbola.html "hyperbola." The Oxford Pocket Dictionary of Current English. 2009. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O999-hyperbola.html |
|
hyperbola
hyperbola Plane curve traced out by a point that moves so that its distance from a fixed point bears a constant ratio, greater than one, to its distance from a fixed straight line. The fixed point is the focus, the ratio is the eccentricity, and the fixed line is the directrix. The curve has two branches and is a conic section. Its standard equation in Cartesian coordinates x and y is x2/a2−y2/b2 = 1.
|
|
|
Cite this article
"hyperbola." World Encyclopedia. 2005. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. "hyperbola." World Encyclopedia. 2005. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O142-hyperbola.html "hyperbola." World Encyclopedia. 2005. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O142-hyperbola.html |
|
hyperbola
hyperbola A type of curve whose two ‘arms’ diverge and never rejoin, defined mathematically as a conic section with an eccentricity greater than 1. The orbit of one body moving past another without being captured has the shape of a hyperbola.
|
|
|
Cite this article
"hyperbola." A Dictionary of Astronomy. 1997. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. "hyperbola." A Dictionary of Astronomy. 1997. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O80-hyperbola.html "hyperbola." A Dictionary of Astronomy. 1997. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O80-hyperbola.html |
|
hyperbola
hyperbola. Conic section formed by the intersection of a plane with both branches of a double cone (two identical cones on either side of the same vertex or pointed top).
|
|
|
Cite this article
JAMES STEVENS CURL. "hyperbola." A Dictionary of Architecture and Landscape Architecture. 2000. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. JAMES STEVENS CURL. "hyperbola." A Dictionary of Architecture and Landscape Architecture. 2000. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O1-hyperbola.html JAMES STEVENS CURL. "hyperbola." A Dictionary of Architecture and Landscape Architecture. 2000. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O1-hyperbola.html |
|
Search over 100 encyclopedias and dictionaries:
HighBeam™ Research, Inc. © Copyright 2012. All rights reserved.
The Encyclopedia.com advertising network includes:
