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