# Hyperbola

An important conic section that is formed due to the interaction of the double cone and a plane surface is known as the hyperbola. It can also be defined as the smooth curve that lies in a plane that resembles two infinite bows. You must note that the interaction of the double and the plane surface may not take place in the center of the surface. This interaction results in the formation of two curved images that are mirror images known as hyperbolas. A hyperbola is made up of various parts. Some of them are foci, center, major and minor axis, and various other parts.

## Properties of a Hyperbola

### The following points analyze the properties of a hyperbola

1.  A hyperbola whose transverse axis and conjugate axis have the same length is known as the rectangular hyperbola.
2.  A hyperbola consists of various points. These points can be expressed or represented with the help of parametric coordinates.
3.  The pair of straight lines that are drawn parallel to the hyperbola is assumed to touch infinity.

### Important Parts of a Hyperbola

To recall, an important conic section that is formed due to the interaction of the double cone and a plane surface is known as the hyperbola. A hyperbola is made up of various parts. Some of them are the major and minor axis, focus, conjugate axis, and so on. The following points are:

1.  A hyperbola is made up of two focuses. The plural of focus is Foci. The coordinates of that focus are, (c, o), and F'(-c, 0).
2.  A point where the two foci meet with each other can be defined as the midpoint or center of the hyperbola. It is also known as the midpoint that joins the two foci of hyperbola.
3.  The length of the axis measuring 2a is known as the major axis. Similarly, the length of the axis measuring 2b units can be defined as the minor axis.
4.  A point where the hyperbola intersects with the axis is known as the vertex. The plural form of the vertex is vertices.
5.  A line that passes through the two foci and midpoint or center of the hyperbola is known as the transverse axis of the hyperbola. Likewise, a line that passes through the two foci and is drawn perpendicularly to the transverse axis is known as the conjugate axis.
6.  The ratio of the distance between the two foci and the midpoint of the hyperbola is defined as the eccentricity of the hyperbola.

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