# Folium of Descartes

#### posix_memalign

How can I eliminate the parameter from the parametric equations of the folium of Descartes?

I.e. I want to go from $$\displaystyle x = \frac{3t}{1+t^3}, y = \frac{3t^2}{1+t^3}$$ to this: $$\displaystyle x^3 + y^3 = 3xy$$

#### Dinkydoe

Try this:

$$\displaystyle x^3+y^3 = \frac{(3t)^3}{(1+t^3)^3}+\frac{(3t^2)^3}{(1+t^3)^3} = \frac{27t^3(1+t^3)}{(1+t^3)^3}=...$$

Can you take it from there?

posix_memalign

#### posix_memalign

Try this:

$$\displaystyle x^3+y^3 = \frac{(3t)^3}{(1+t^3)^3}+\frac{(3t^2)^3}{(1+t^3)^3} = \frac{27t^3(1+t^3)}{(1+t^3)^3}=...$$

Can you take it from there?
Yes, thank you.