Today, actually just an hour or so ago, another math teacher asked me if I knew a way to parametrize the following:
It is also known as the Folium of Descartes and looks like:
Her purposes was just trying to find a quick and easy way to graph it on the calculator. It was just a small, unimportant question. She didn’t need to know the answer, if it wasn’t easily doable. But to me, I needed to know! How do we find the parametric equations which define this? I just don’t know. The answer I found online is:
And it’s pretty easily verifiable when you work backwards with the parametrization.
Is there something I’m missing? Is there a method to working from implicitly defined 2D functions to parametrizations for them?