Represent the parabola y=x^{2}+1 by a vector-valued function

rescuedbyhimw0 2021-11-23 Answered
Represent the parabola \(\displaystyle{y}={x}^{{{2}}}+{1}\) by a vector-valued function

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Expert Answer

Jeffrey Parrish
Answered 2021-11-24 Author has 6881 answers

Step 1
Given Parabola
\(\displaystyle{y}={x}^{{{2}}}+{1}\)
The Vector valued function is
\(\overrightarrow{r}(t)=x(t)\hat{i}+y(t)\hat{j}\)
Step 2
In Parabola eqn, y is explicity defined in terms of x
\(\displaystyle\therefore{x}={t}\)
\(\displaystyle{y}={t}^{{{2}}}+{1}\)
Ans: \(\overrightarrow{r}(t)=t\hat{i}+(t^{2}+1)\hat{j}\)

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