Different Types of Hyperbolas

There are two types of hyperbolas one hyperbola has conjugate axis is X-axis and other has conjugate axis is Y-axis. In the given table we explain different components and graphs of ellipse.

Standard Hyperbolas

Equation

\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}}    = 1

\frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}}    = 1

Focus

\left( { \pm ae,0} \right)

\left( {0, \pm ae} \right)

Directrices

x = \pm    \frac{a}{e}

y = \pm    \frac{a}{e}

Major Axis

y = 0

x = 0

Vertices

\left( { \pm a,0} \right)

\left( {0, \pm a} \right)

Co-Vertices

\left( {0, \pm b} \right)

\left( { \pm b,0} \right)

Centre

\left( {0,0} \right)

\left( {0,0} \right)

Eccentricity

e = \frac{{\sqrt {{a^2} + {b^2}} }}{a}

e = \frac{{\sqrt {{a^2} + {b^2}} }}{a}

Length of Latus Rectum

\frac{{2{b^2}}}{a}

\frac{{2{b^2}}}{a}

Graph

hyperbola-01

hyperbola-02

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