Different Types of Ellipses

There are two types of ellipses: one ellipse has the X-axis as the major axis and the other has the Y-axis as the major axis. In the given table we explain different components and graphs of ellipses.

Standard Ellipses

Equation
\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1,\,\,\,a > b
\frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1,\,\,\,a > b
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},\,\,\,a > b
e = \frac{{\sqrt {{a^2} - {b^2}} }}{a},\,\,\,a > b
Length of Major Axis
2a
2a
Length of Minor Axis
2b
2b
Length of Latus Rectum
\frac{{2{b^2}}}{a}
\frac{{2{b^2}}}{a}
Graph
ellipse-01
ellipse-02