TITLE: Help finding equation for my calculus class
QUESTION [0 upvotes]: 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!

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