A hyperbola is a curve with two mirror image branches that goes on forever. It is not to be confused with hyperbole, a literary concept. Hyperbolas have two focal points and are used in technology and space.
A hyperbola is a mathematical term for a curve in a plane that has two branches that are mirror images of each other. Like the similar parabola, the hyperbola is an open curve that has no end. This means that in theory it will go on forever, unlike the circle or ellipse.
This is not to be confused with the literary term hyperbole. Both terms come from a Greek word that translates to “overturned” or “excessive.” However, hyperbole is a literary concept that describes a statement that is greatly exaggerated for emphasis. It is most common seen in poetry or casual speech. The term hyperbole is generally thought to have been coined by Apollonius of Perga in his work with conics.
Cones have four curves called conics, which include hyperbolas and parabolas, as well as circles and ellipses. Each section is defined by its eccentricity, or how far it deviates from being a circle. For example, the eccentricity of a circle is zero. The eccentricity of a hyperbola is greater than one and the eccentricity of the parabola is less than one. On the other hand, the eccentricity of an ellipse is less than one but greater than zero.
A hyperbola has several characteristics. It has two focal points, which can also be called foci. These two points are connected by a line called the transverse axis, and the midpoint of that line marks the center of the hyperbola. Also, the line which is perpendicular to the cross axis is called the conjugate axis. Together the conjugate axis and the transverse axis form the two principal axes of the hyperbola. These two axes are important, because a parabola must be symmetrical on both of these lines.
Hyperbolas have applications outside the theoretical world. Let’s take for example a water ripple that forms concentric circles. When these circles intersect, they form hyperbolas. Both sound and light waves mimic this behavior. Radar is a particular area of technology that uses hyperbole in its scientific reasoning.
Hyperbolas can also be found in space. Orbiting planets or moons follow an elliptical orbital path. However, any object that passes through a solar system and doesn’t orbit it will follow a hyperbolic path. A comet is an example of a hyperbolic path through space.
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