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

enter image description here

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!

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    It looks like the [Folium of Descartes](http://www-history.mcs.st-and.ac.uk/Curves/Foliumd.html) – 2017-02-21
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    @pjs36 yes! thanks! – 2017-02-21
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    Could also be a part of any of several [trisectrix](https://en.wikipedia.org/wiki/Trisectrix) flavors. – 2017-02-21

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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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    yes! that's it! – 2017-02-21