Focus

The fixed point is called a focus F1(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 L1 and L1′ are the end points of one latus rectum, then

L1 = (ae, b2/a)

L1′ = (ae, −b2/a)