(a) Find a vector-parametric equation for the loop of the folium of Descartes curve $x^3 + y^3 = 3 x y$ by letting $P$ be the point of intersection of the line $y = t x$ with the loop and solving for the coordinates of $P$. $\vec{r}(t) =$ for all $t$ in the interval (b) Is the loop parametrized clockwise or counterclockwise? Choose Clockwise Counterclockwise (c) As $t \to \infty$, does the point $P$ speed up, slow down, or travel at a constant speed? Choose Speed up Slow down Constant Speed

The folium of Descartes

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