# Represent the plane curve by a vector-valued function y=9-x^{2}

Represent the plane curve by a vector-valued function
$$\displaystyle{y}={9}-{x}^{{{2}}}$$

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Warajected53
Step 1
Let us find the plane curve by a vector-valued function
Given:
$$\displaystyle{y}={9}-{x}^{{{2}}}$$
The vector valued function for a plane curve:
$$\displaystyle{r}{\left({t}\right)}={x}{\left({t}\right)}{i}+{y}{\left({t}\right)}{j}$$
Step 2
$$\displaystyle{x}{\left({t}\right)}={t}$$
$$\displaystyle{y}{\left({t}\right)}={9}-{t}^{{{2}}}$$
$$\displaystyle{r}{\left({t}\right)}={t}{i}+{\left({9}-{t}^{{{2}}}\right)}{j}$$