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anonymous 5 years ago How to parameterize a folium curve (x^3 + y^3 - 9xy = 0)?

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1. anonymous

Consider if you set y=tx. Then plugging this in, you have $x^3+x^3t^3-9tx^2=x^2(x(t^3+1)-9t)=0$ Thus since x is not identically zero, you have that $x(t^3+1)-9t=0 \implies x=\frac{9t}{t^3+1}$ Since y=tx, this give you also $y=tx=\frac{9t^2}{t^3+1}$ This parametrizes your folium.

2. anonymous

Thanks, that's it.

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