Algebra/Ellipse

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


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