Difference between revisions of "Hyperbola"
Conservateur (talk | contribs) (New page: A '''hyperbola''' is a curve produced by the intersection of a plane with both nappes of a conic section. == Mathematical definition == A hyperbola may be more formally defined as th...) |
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== Mathematical definition == | == Mathematical definition == | ||
A hyperbola may be more formally defined as the locus of all points the difference of whose distances from two fixed points (the foci) is constant. The [[Cartesian]] equation for a hyperbola with a semimajor axis about the x-axis is | A hyperbola may be more formally defined as the locus of all points the difference of whose distances from two fixed points (the foci) is constant. The [[Cartesian]] equation for a hyperbola with a semimajor axis about the x-axis is | ||
| − | < | + | :<math>x^2/a^2 - y^2/b^2 = 1 </math> |
| − | x | ||
| − | </ | ||
== Applications == | == Applications == | ||
[[Nuclear reactor]] cooling towers are an example of a hyperbolic-shaped structure. This form allows for maximum structural strength with minimum use of building materials. | [[Nuclear reactor]] cooling towers are an example of a hyperbolic-shaped structure. This form allows for maximum structural strength with minimum use of building materials. | ||
When two [[rock]]s are thrown simultaneously into a pool of still [[water]], ripples move outward in concentric [[circle]]s. These circles intersect in points which form a curve known as the hyperbola. The same phenomenon is used in [[radio]] tracking stations. Objects are located by sending out signals from two sources to a receiving station, such as one found on a [[boat]] or [[airplane]]. The constant time difference between the signals from the two stations is represented by a hyperbola. | When two [[rock]]s are thrown simultaneously into a pool of still [[water]], ripples move outward in concentric [[circle]]s. These circles intersect in points which form a curve known as the hyperbola. The same phenomenon is used in [[radio]] tracking stations. Objects are located by sending out signals from two sources to a receiving station, such as one found on a [[boat]] or [[airplane]]. The constant time difference between the signals from the two stations is represented by a hyperbola. | ||
Revision as of 23:27, August 1, 2007
A hyperbola is a curve produced by the intersection of a plane with both nappes of a conic section.
Mathematical definition
A hyperbola may be more formally defined as the locus of all points the difference of whose distances from two fixed points (the foci) is constant. The Cartesian equation for a hyperbola with a semimajor axis about the x-axis is
Applications
Nuclear reactor cooling towers are an example of a hyperbolic-shaped structure. This form allows for maximum structural strength with minimum use of building materials.
When two rocks are thrown simultaneously into a pool of still water, ripples move outward in concentric circles. These circles intersect in points which form a curve known as the hyperbola. The same phenomenon is used in radio tracking stations. Objects are located by sending out signals from two sources to a receiving station, such as one found on a boat or airplane. The constant time difference between the signals from the two stations is represented by a hyperbola.