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 4x^{2} + y^{2} = 16

Learn how to derive that c^{2} = a^{2} - b^{2} 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 5x^{2} + 9y^{2} = 45

Find the equation of an ellipse given the eccentricity and the foci.

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

How to graph an ellipse?

Learn the eccentricity 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).

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 4x

Learn how to derive that c

\(e = \frac{c}{a}{\rm{ }}\) where \(c = \sqrt {{a^2} - {b^2}} \)

Find the eccentricity and foci of the ellipse 5x

Find the equation of an ellipse given the eccentricity and the foci.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.