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Hyperbola: Standard Equations and Eccentricity


What is Hyperbola?

It is the set of all points in a plane, the minus of whose distances from two fixed points in the plane is constant.

The fixed points F1 and F2 are called the foci of the hyperbola.

Hyperbola Standard Equations

Center of the hyperbola

The midpoint of the line segment joining the foci is called center of the hyperbola.

In the given figure, F1 and F2 are the foci of the hyperbola and O is its centre,

OF1= OF2

Axis of the Hyperbola

The path into the foci of the hyperbola is called its transverse axis.

In the figure, X’OX is the transverse axis of the hyperbola.

The line through the centre and perpendicular to the transverse axis of the hyperbola is called the conjugate axis.

In the figure, COD is the conjugate axis of the hyperbola.

Vertices of the Hyperbola

The points at which the hyperbola intersects the transverse axis are called its vertices.

Given figure, A and B are the vertices of the hyperbola.

Length of the Transverse axis

The distance between the two vertices of a hyperbola is called the length of its Transverse axis.

Length of the Transverse axis AB = 2b

Standard Equation of Hyperbola

Equation of Hyperbola

Latus Rectum of a Hyperbola

The latus rectum of a hyperbola is a line segment perpendicular to the transverse axis, through any of the foci with its

endpoints lying on the hyperbola.

Length of the Latus Rectum = 2b 2/a