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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...
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
<blockquote>
x<sup>2</sup>/a<sup>2</sup> - y<sup>2</sup>/b<sup>2</sup> = 1
</blockquote>
== 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 [[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.
== 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
<blockquote>
x<sup>2</sup>/a<sup>2</sup> - y<sup>2</sup>/b<sup>2</sup> = 1
</blockquote>
== 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 [[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.