Conic Sections: Hyperbolas

Graphing a Hyperbola Centered at the Origin

Once again there are two cases for hyperbolas centered at the origin. The following are the two standard equations of a hyperbola.

Horizontal Transverse Axis

Horizontal hyperbola with vertices, co-vertices, and foci labeled.

x squared divided by a squared minus y squared divided by b squared equals 1

a2 + b2 = c2

The length of the transverse axis is 2a.

The length of the conjugate axis is 2b.

Vertical Transverse Axis

Horizontal hyperbola with vertices, co-vertices, and foci labeled.

y squared divided by a squared minus x squared divided by b squared equals 1

a2 + b2 = c2

The length of the transverse axis is 2a.

The length of the conjugate axis is 2b.