AS/A2 Pure 4 Pure 6

P5 Topic 1: Coordinate Systems
The hyperbola
The hyperbola is an example of a conic section. The illustration comes from Jill Britton. In the display below use your mouse to change the values of a and b. The graph displayed is an hyperbola. It is described by the Cartesian equation: This equation does not give y explicitly in terms of x, and so is called an implicit equation in x and y. Also displayed in red are the asymptotes of the hyperbola. These have equations:

Summary For the hyperbola, the main axes are also axes of symmetry. The one along the x axis is called the transverse axis and the one along the y axis is called the conjugate axis. Note that if you equalize the axes and then make a and b the same, a rectangular hyperbola is displayed (zoom out to see this more clearly). Based on free Java applets from JavaMath