find an equation of the curve $ \vec{c}(t) $in cartesian

Question

find an equation of the curve $ \vec{c}(t)$ in $cartesian$ coordinates and sketch its graph $\vec{c}(t) = (t+4)\vec{i} +t^{2}\vec{j}$ ; $ t\in [1,3]$

How to start?

Answer 1

We have $\vec{c}(t)=(x(t),y(t))$ with $x(t)=t+4$ and $y(t)=t^2$. Therefore

$t=x(t)-4$, hence

$y(t)=(x(t)-4)^2$.

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