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

Redemitz4s 2021-11-21 Answered
Represent the plane curve by a vector-valued function
\(\displaystyle{y}={9}-{x}^{{{2}}}\)

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Expert Answer

Warajected53
Answered 2021-11-22 Author has 106 answers
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
\(\displaystyle{x}{\left({t}\right)}={t}\)
\(\displaystyle{y}{\left({t}\right)}={9}-{t}^{{{2}}}\)
\(\displaystyle{r}{\left({t}\right)}={t}{i}+{\left({9}-{t}^{{{2}}}\right)}{j}\)
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