AS/A2 Pure 4 Pure 6

P5 Topic 1: Coordinate Systems
The ellipse
The ellipse is an example of a conic section. The illustration comes from Jill Britton. In the diaplay below use your mouse to change the values of a and b. The graph displayed is an ellipse. 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.

Summary The ellipse has two diameters that are axes of symmetry. The longer one is called the major axis and the shorter one is called the minor axis. Note that if you equalize the axes and then make a and b the same, a circle is displayed. Based on free Java applets from JavaMath