# Hyperbola

The hyperbola is the locus of points on the plane whose difference of distances to two fixed points, foci, are constant.

### Elements of the Hyperbola

**Foci**

The foci are the fixed points of the hyperbola. They are denoted by **F ** and **F'**.

**Transverse Axis** or real axis

The tranverse axis is the line segment between the foci.

**Conjugate Axis** or imaginary axis

The conjuagate axis is the perpendicular bisector of the line segment (transverse axis).

**Center **

The center is the point of intersection of the axes and is also the center of symmetry of the hyperbola.

**Vertices**

The points A and A' are the points of intersection of the hyperbola with the transverse axis.

**Focal Radii**

The focal radii are the line segments that join a point on the hyperbola with the foci: **PF** and **PF'**.

**Focal Length**

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

**Semi-Major Axis**

The semi-major axis is the line segment that runs from the centre to a vertex of the hyperbola. Its length is **a**.

**Semi-Minor Axis**

The semi-minor axis is a line segment which is perpendicular to the semi-major axis. Its length is **b**.

**Axes of Symmetry**

The axes of symmetry are the lines that coincide with the transversal and conjugate axis.

**Asymptotes**

The asymptotes are the lines with the equations:

**The Relationship between the Semiaxes**: