The focus of a lens
or parabolicmirror
is the point onto which collimated light parallel to the axis is focused. The
focus of an elliptic mirror
is either of two points such that light from one converges on the other. The
focus of a hyperbolic
mirror is either of two points such that light from one is reflected as if it
came from the other.
Geometry
In an ellipse, foci are the two "off-center" points.