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 |
Mrs Beverly Utly
March 20 @ 2:18 am
Is the formula for latus rectum both the equations same?