An ellipse is a conic section where a plane intersects a right circular cone at an angle, and looks like an oval.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Our lesson begins with an understanding of the major characteristics of an ellipse in standard form.
We quickly see that there is some symmetry to an ellipse, and we represent that by indicating the major axis (segment along the longest part of the ellipse that connects the two vertices) and the minor axis (segment along the shortest part of the ellipse that connects the two co-vertices).
Similarly, we will come to see that each and every ellipse is generated from two fixed points called foci, as Purple Math nicely states.
Graph of Ellipse
Together we will learn how to sketch an ellipse centered at the origin and find all:
- vertices
- co-vertices
- foci
- length of the major and minor axes
Then we will learn how to write the equation of an ellipse, in standard Form, given points on the ellipse.
Next, we will discover how to translate an ellipse by moving our center to (h,k) and from there find our vertices, co-vertices, and foci.
Finally, we will take an ellipse equation in general (expanded) form and use the technique of completing the square to rewrite it in standard form in order to sketch the ellipse and determine the domain and range.
How to Classify Ellipses (Conics) – Video
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