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If you have worked through the Ellipse Module, you know that an ellipse can be described by the standard equation: x2 + y2 = 1 a2 b2

Another way to describe an ellipse is as the locus of points such that the sum of the distances from one point, P, to two fixed points, F1 and F2, is constant.

The two fixed points are called the focal points or foci.

In the below action figure, notice where the focal points, F1 and F2, are located in the ellipse. Note that the distance PF1 is represented by a blue line segment, while the distance PF2 is represented by a green line segment.

As you click and drag point P on the ellipse, the graph on the right hand side of the action figure shows the summed distance of the blue and green line segments for any point P on the ellipse.

What happens if the focal points or foci are moved?

Answer the questions in the question box below to guide your explorations.