Help finding equation for my calculus class

Question

I mentioned in my class that an equation could describe a curve like this:

I drew the curve so that the crossing point was at the origin $(0,0)$, and the loop was in the first quadrant. Can you give an equation that would describe a curve like this?

Thanks!

Answer 1

Try the "Folium of Descartes". The equation is $$x^3+y^3-3axy=0.$$ In polar coordinates is $$r=\frac{3a\sin\theta\cos\theta}{\sin^3\theta+\cos^3\theta}.$$