# Ellipses

A series of free Intermediate Algebra Lessons.
How to write the equations of an ellipse?
How to graph an ellipse?
Learn the eccentricity of an ellipse.

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).
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.

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.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.