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In the Hyperbola Module, you learned that the standard equations of a hyperbola centred at the origin are: x2 - y2 = 1     or     - x2 + y2 = 1 a2 b2 a2 b2 depending on whether the vertices lie on the horizontal or vertical axes.

As with circles and ellipses, hyperbolas can be descibed as a locus of points satisfying some special condition. This special condition for hyperbolas is that the difference of the distances between a point P on the hyperbola, and two fixed points F1 and F2 is constant.

The two fixed points, F1 and F2 are again called the focal points or foci of the hyperbola.

Notice that the locus definition of hyperbola is very similar to that of ellipses, with hyperbolas having a constant difference property, and ellipses having a constant sum property.