Algebra/Ellipse

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Algebra
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Ellipse Animation Small.gif
Ellipse axis.png

An ellipse is the collection of points that are equidistant from two points, called foci (singular focus).

The foci are found on the major axis, which has a length of 2a. The minor axis is 2b, and is smaller.

The "roundness" or "longness" of an ellipse can be measured by eccentricity. If c is the distance from the center to a focus, then e = c / a.

The latus rectum is a line parallel to the minor axis that crosses through a focus. Its length is b2 / a.

"Long" ellipses are generally written as

\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1

where (h,k) is the center, while "tall" ellipses are written as

\frac{(y-k)^{2}}{a^{2}} + \frac{(x-h)^{2}}{b^{2}} = 1