Conic Section, Rectangular Hyperbola, Transverse Axis, Conjugate Axis

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In this case: Transverse axis is along y-axis and conjugate axis is along x-axis.

In case of Hyperbola example

In Case of Hyperbola Example

In case of Hyperbola example

Length of transverse axis.

Length of conjugate axis

Length of latus rectum

Equations of directrices

Vertices

Foci

Centre

Eccentricity

Rectangular Hyperbola

If in a hyperbola the length of the transverse axis is equal to the length of the conjugate axis, then the hyperbola is called a rectangular hyperbola.

Its equation is or

In this case or

I.e. the eccentricity of rectangular hyperbola is

Example 1:

For the hyperbola, find the following (i) Eccentricity (ii) Foci (iii) Vertices (iv) Directrices (v) Length of transverse axis (vi) Length of conjugate axis (vii) Length of latus rectum (viii) Centre.

Solution:

Here and 9, and

Eccentricity

Foci

Vertices

Directrices

Length of transverse axis

Length of conjugate axis

Length of latus rectum

Centre

Example 2:

Find the equation of hyperbola with vertices and foci

Solution:

Here and

We know that

Equation of hyperbola is

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