Ellipses

An ellipse is a conic section that resembles a stretched or compressed circle. It is defined as the set of all points in a plane such that the sum of their distances from two fixed points (called the foci) is constant. The standard equation of an ellipse depends on its orientation (horizontal or vertical) and the location of its center.

How to write the equations of an ellipse?
How to graph an ellipse?
Learn the eccentricity of an ellipse.

The following diagram gives the standard form for the equation of an ellipse with center (0,0). Scroll down the page for more examples and solutions.

 

Writing the Equation of an Ellipse
Learn the standard form for the equation of an ellipse with center (0, 0)
How to write the equation of the ellipse given the graph.
Write the equations of the ellipse with vertex (0, 7) and the co-vertex (4, 0).

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Graphing Ellipses
Horizontal ellipse and vertical ellipse
Example 1: Graph the ellipse \(\frac{{{x^2}}}{9} + {y^2} = 1\) and find the x-intercepts and y-intercepts
Example 2: Graph the ellipse 4x² + y² = 16
Learn how to derive that c² = a² - b² for the ellipse.

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The Eccentricity of an Ellipse
\(e = \frac{c}{a}{\rm{ }}\) where \(c = \sqrt {{a^2} - {b^2}} \)
Find the eccentricity and foci of the ellipse 5x² + 9y² = 45
Find the equation of an ellipse given the eccentricity and the foci.

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