The ellipse is the locus of points on the plane whose sum of distances to two fixed points, foci, are always constant.
Elements of the Ellipse
The foci are the fixed points of the ellipse which are located on the major axis. They are denoted by F and F'.
The major axis of the ellipse is the line segment , which has a length of 2a.
The major axis coincides with the major diameter and passes through the center point and both foci.
The minor axis of the ellipse is the line segment , which has a length of 2b.
The minor axis is the perpendicular bisector of the major axis.
The focal length of the ellipse is the line segment , which has a length of 2c.
The center of the ellipse is the point of intersection of the axes. It is the center of symmetry of the ellipse.
The vertices of the ellipse are the points of intersection of the ellipse with the axes. They are denoted by A, A', B and B'.
The focal radii are the line segments that join a point on the ellipse with both foci. They are denoted by PF and PF'.
The semi-major axis is the line segment that runs from the centre of the ellipse, through a focus, and to a vertex of the ellipse. Its length is a.
The semi-minor axis is the line segment, perpendicular to the semi-major axis, that runs from the centre of the ellipse to a vertex. Its length is b.
If a = b, an ellipse is more accurately defined as a circle.
Axes of Symmetry
The axes of symmetry are the lines that coincide with the major and minor axes.
Relationship between the Semiaxes