# Focus of an ellipse

If $A$ and $B$ are two points, then the locus of points $P$ such that $AP + BP = c$ for a constant $c>2 AB$ is an ellipse. $A$ and $B$ are the foci (plural of focus) of this ellipse.

If an ellipse has centre $(0,0)$, eccentricity $e$ and semi-major axis $a$ in the $x$-direction, then its foci are at $(\pm ae, 0)$ and its directrices are $x=\pm a/e$.