The ellipse is defined as the locus of a point (x,y) which moves so that the sum of its distances from two fixed points (called foci, or focuses) is constant.
We can produce an ellipse by pinning the ends of a piece of string and keeping a pencil tightly within the boundary of the string, as follows.
We start with these 2 foci:
We pin the ends of the string to the foci and begin to draw, holding the string tight:
Our complete ellipse is formed: