Different Types of Ellipses

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

Centre

\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

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