You will go through the concept of hyperbola in the chapter of conic sections. In mathematics, when a double cone is intersected by a plane surface, one of the important conic sections, hyperbola, is formed. This intersection need not be necessarily at the center. We can apply the concepts like directrix, eccentricity, latus rectum, foci, etc in a hyperbola. Some real-life examples of the hyperbola are as follows: cooling towers of nuclear plants, certain types of buildings, the orbits of some heavenly bodies, etc. In this article, we will discuss in detail hyperbola and its various applications.

## Equation of a Hyperbola

We can represent the equation of a hyperbola in the given manner:

x.x/a.a – y.y/b.b = 1 where the y axis represents the conjugate axis of the given hyperbola and the x-axis represents the transverse axis of the given hyperbola.

### Applications of the Hyperbola

There are various applications related to the hyperbola which are discussed as follows:

• Used As Cooling Towers: The shape of hyperbola also known as the hyperboloid is the basic shape in which cooling towers of nuclear power plants and some power plants of coal are designed. It is because hyperbola solved two basic problems of the engineers designing the tower. First, the structure must be designed in such a manner that it is able to withstand high and powerful winds. Second, the structure should be designed in such a manner that it uses the minimum material possible.
• Used in Location of Position Using the Technique of Trilateration: A technique in which the location of an exact position is calculated by calculating the distance between a set of two points is called trilateration. Problems of trilateration are solved using the idea of a hyperbola.
• Creation of Dulles Airport: Dulles Airport of Virginia, USA is designed in the shape of a hyperbolic paraboloid. Many other man-made buildings are designed around the world in similar shapes.
• Sonic Boom Curve: During the year 1953, a plane flew faster than the speed of sound. A hyperbola was formed during the intersection of the comic-like wave with the ground. A conic-like wave was created because the plane moved faster than the speed of sound. Sonic boom made a connection and hit every point on the curve at the same time. The hyperbola that was created is known as the sonic boom curve. An interesting fact to know about this curve is that one cannot hear any sound outside the curve.

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The shape of the hyperbola can be seen in sundials. Many other concepts of the subject of physics employ the use of the conic section, hyperbola. If you want to learn more about these complex topics of hyperbolas and conic sections in detail and in a fun and interesting manner, visit Cuemath.

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