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'Ellipses' printed from http://nrich.maths.org/

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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.