Different Types of Hyperbolas

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

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)
Center
\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