Here is a pattern for you to experiment with using graph drawing software. For example, you can download Graphmatica for free from here and it comes with a good Help file.

graph.

The equations of two of the graphs are:

\frac{x^{2}}{36} + \frac{y^{2}}{16} = 1

x^{2} + y^{2} = 1

Find the equations of the other 8 graphs in this pattern.
How do you know from their equations that all the graphs are symmetrical about both the y-axis and the x-axis?

Draw your own pattern of ellipses and circles.