To do this, we can set $t^{2}=u$ and $t^{3}=v$ in $\mathbf{r}(t)$ to get $\mathbf{r}(u,v)=\left\langle u,v\right\rangle$. Similarly, setting $t^{4}=u$ and $t^{6}=v$ in $\mathbf{r}_{1}(t)$ gives $\mathbf{r}_{1}(u,v)=\left\langle u^{2},v^{2}\right\rangle$. We can
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