Course: College Algebra
Topic: Conic Sections
Subtopic: Ellipses


One of the conic section curves is the ellipse. Ellipses are circles that have been stretched horizontally or vertically to make an oval like shape. They are formed based on the placement of two interior focal points rather than one center point. Ellipses are rich in scientific history. Fun research might include Kepler's Laws of Planetary Motion.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: ellipse, standard form (e.g. `(x-h)^2/a^2+(y-k)^2/b^2=1`), focal points (foci), vertices, major axis, minor axis, eccentricity

Text Notes

Be sure that you understand the process of converting a general form conic to a standard form conic via complete the square. This process will be used throughout the chapter on conics. Note that the CTS process shown in this chapter is slightly different than the CTS process of solving a quadratic equation because a conic's equation may contain both x's and y's that are squared and thus require that you CTS on the x and CTS on the y.

Supplemental Resources (recommended)

Explore the interactive graphs at Interactive Ellipse Graphs which show how the ellipses's focal points form the ellipse's oval shape. The Ellipse has a couple nice applications of ellipses, worth skimming.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics: "Graphing and Writing Equations of Ellipses".

rev. 2020-11-29