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Focus

A focus is a point used to construct a conic section.  (The plural is foci.)  The focus points are used differently to determine each conic.

           A circle is determined by one focus. A circle is the set of all points in a plane at a given distance from the focus (center).

           A parabola is determined by a focus and a directrix (a line).  A parabola is the set of points in a plane such that the distance from the focus equals the distance to the directrix.

           An ellipse is determined by two foci.  An ellipse is the set of points in a plane such that the sum of the distance from a point to each focus is constant.

           A hyperbola is determined by two foci.  A hyperbola is the set of points in a plane such that the difference between the distances from a point to each focus is constant.