Difference between revisions of "Hyperbola"

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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>
+
:<math>\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 </math>
 +
 
 
== 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.

Latest revision as of 14:22, 14 December 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.