# Ellipse

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

**Foci**

The foci are the fixed points of the ellipse which are located on the major axis. They are denoted by **F ** and **F'**.

**Major Axis**

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.

**Minor Axis **

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.

**Focal Length**

The focal length of the ellipse is the line segment , which has a length of ** 2c**.

**Center**

The center of the ellipse is the point of intersection of the axes. It is the center of symmetry of the ellipse.

**Vertices**

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'**.

**Focal Radii**

The focal radii are the line segments that join a point on the ellipse with both foci. They are denoted by **PF** and **PF'**.

**Semi-Major Axis**

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**.

**Semi-Minor Axis **

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