Difference between revisions of "Hyperbola"
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A '''hyperbola''' is a curve produced by the intersection of a plane with both nappes of a [[conic section]]. | A '''hyperbola''' is a curve produced by the intersection of a plane with both nappes of a [[conic section]]. | ||
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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 | + | :<math>\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 </math> |
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== 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 [[ship|boat]] or [[airplane]]. The constant time difference between the signals from the two stations is represented by a hyperbola. |
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| + | [[Category:Geometry]] | ||
Latest revision as of 19:22, December 14, 2016
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.