Definition

A hyperbola is the collection of all points in the plane, the difference of whose distances from two fixed points is a constant. Alternatively, a hyperbola is the collection of all points in the plane, whose distances from a fixed point in the plane bears a constant ratio greater than one to their distance from a fixed line in the plane.

Here difference in the definition means, the distance to the farther point minus the distance to the closer point.

The fixed point is called a focus and the fixed line as directrix and the constant ratio (denoted by e) the eccentricity of the hyperbola.

The figure given below, illustrates a hyperbola with foci F1 and F2.

• The line containing the foci is the transverse axis.
• The mid-point of the line segment joining the foci is called the centre of the hyperbola.
• The line through the centre, which is perpendicular to the transverse axis is called the conjugate axis.
• The hyperbola consists of two separate curves (called branches), which are symmetric with respect to the transverse axis, the conjugate axis and the centre.
• The two points of intersection of the hyperbola and the transverse axis are called the vertices V1 and V2 of the hyperbola.