Written by the Fiveable Content Team • Last updated August 2025
Written by the Fiveable Content Team • Last updated August 2025
Definition
An ellipse is a set of all points in a plane where the sum of the distances from two fixed points (foci) is constant. It is an important type of conic section.
The standard form equation of an ellipse centered at the origin: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
In the standard form, if $a > b$, the major axis is along the x-axis; if $b > a$, it is along the y-axis.
The distance between the center and each focus is given by $c = \sqrt{a^2 - b^2}$ for horizontal ellipses and $c = \sqrt{b^2 - a^2}$ for vertical ellipses.
The eccentricity of an ellipse, denoted as $e$, measures its deviation from being circular and is calculated as $e = \frac{c}{a}$ for horizontal ellipses or $e = \frac{c}{b}$ for vertical ellipses.
An ellipse has two axes of symmetry: the major axis (longest diameter) and minor axis (shortest diameter).