A hyperbola is a geometrical figure which is a combination of two open curves each having two branches. The two curves are like mirror images of each other. Each of the curves has a focus and the vertex of one curve faces the other. The foci of the hyperbola are the fixed points that are situated inside each curve of a hyperbola and if connected, form a horizontal line. The hyperbola is the graph created by joining a series of points such that the difference between the distances from each point to the two foci is constant. This difference is taken by the distance from the farther focus and the distance from the nearer focus.

For example, if P(x, y) is a point on the hyperbola and for two foci F1 (farther) and F2 (nearer),

then PF – PF’ = constant.

Parts of a Hyperbola

A hyperbola has different parts which are mentioned as follows:

Foci: The two fixed points from which the difference of distances from any point on the hyperbola has a constant value. 

Center: The middle point of the line joining the two foci is called the center of the hyperbola.

Major Axis: The horizontal line joining the two foci is called the major axis.

Minor Axis: The vertical line passing through the center of the hyperbola is called the minor axis.

Vertices: The two points where the hyperbola intersects the axis are the vertices of the hyperbola.

Transverse Axis: The line segment on the major axis whose endpoints are two vertices is called the transverse axis.  

Conjugate Axis: The line segment of the minor axis whose endpoints are equidistant from the center of the hyperbola.

The eccentricity of Hyperbola: The ratio of the distance of the focus from the center, and the distance of the vertex from the center of the hyperbola. 

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