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Concept

Ellipse

An ellipse is the set of points in a plane such that the sum of the distances from two fixed points is constant. These two points are called the foci of the ellipse. In the figure, the sum of the distances from the foci and to a point on the ellipse is
ellipse

All ellipses have important key features.

  1. The vertices of an ellipse are the intersection points between the ellipse and the line passing through the foci.
  2. The major axis of an ellipse is the segment connecting the vertices.
  3. The center of an ellipse is the midpoint of the major axis.
  4. The co-vertices of an ellipse are the intersection points between the ellipse and the line perpendicular to the major axis at the center of the ellipse.
  5. The minor axis of an ellipse is the segment connecting the co-vertices.

The above information can be illustrated in a diagram.

Ellipse with all its parts highlighted

If the major axis of an ellipse is horizontal, the ellipse is called a horizontal ellipse. Conversely, if the major axis is vertical, the ellipse is called a vertical ellipse. Below are the general equations for these two types of ellipses.

In these equations, and are half the lengths of the major and minor axes, respectively. Furthermore, in both cases, is the center of the ellipse.

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