Food for thought

## Suggestion

The image in the warm-up shows one of a family of functions represented by the implicit equation $(x^2+2ay-a^2)^2=y^2(a^2-x^2)$.

Try changing $a$ using the slider in the applet below.

What do you notice about the other functions in the family?

Are there any questions that you would like to ask about the images and the equation?