Folium of Descartes

May 2008
87
0
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: \(\displaystyle x^3 + y^3 = 3xy\)
 
Dec 2009
411
131
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?
 
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