Definition

We begin this section with the definition of an ellipse. An ellipse is the set of all points (x, y) in the plane such that the sum of the distances from (x, y) to two fixed points is some constant. The two fixed points are called the foci, which is the plural of focus. (See FIGURE E1 for the graph of an ellipse with the foci included.)

Note that this is clearly a geometrical definition and does not point out the relationship between an ellipse and its algebraic equation.