# Important Definitions Regarding Hyperbola

**Focus **

The fixed point is called a focus F_{1}(ae, 0) of the hyperbola.

**Directrix **

The fixed line is called the directrix of the hyperbola and its equation is x = a/e.

**Transverse Axis**

The line segment AA′ joining the vertices is called the transverse axis and the length of the transverse axis is 2a.

The equation of transverse axis is y = 0. The transverse axes cut both the branches of the curve.

**Conjugate Axis**

The line segment joining the points B(0, b) and B′(0, −b) is called the conjugate axis. The length of the conjugate axis is 2b.

The equation of the conjugate axis is x = 0.

**Centre**

The point of intersection of the transverse and conjugate axes of the hyperbola is called the centre of the hyperbola. C(0, 0) is called the centre of the hyperbola.

**Vertices**

The points of intersection of the hyperbola and its transverse axis is called its vertices. The vertices of the hyperbola are A(a, 0) and A′(−a, 0).

**Latus Rectum **

It is a focal chord perpendicular to the transverse axis of the hyperbola. The equations of the latus rectum are x= ±ae.

If L_{1} and L_{1}′ are the end points of one latus rectum, then

L_{1} = (ae, b^{2}/a)

L_{1}′ = (ae, −b^{2}/a)