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