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?
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Hint: write $x=t-4, y=t^2$ and try to find an expression like $y=f(x)$ – user438666 May 31 '17 at 08:52
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yea i did that before but i do not know what next, or how yo graph it @Chris – sh.alzoubi May 31 '17 at 08:54
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2what did you get? – user438666 May 31 '17 at 08:56
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@sh.alzoubi If you did that before, you should have said that you did so in the body of your question so that we do not repeat information you already know. Please include all your thoughts about the problem and what you've tried in the body of every question you ask. – projectilemotion May 31 '17 at 09:18
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1Do you know how to find $t$ from $x=t+4$? – Emilio Novati May 31 '17 at 09:21
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The concept is the same as in this video. – projectilemotion May 31 '17 at 09:21
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@Chris On your first comment, I think you mean $x=t\color{red}{+}4$. This is a typographical error, correct? – projectilemotion May 31 '17 at 09:29
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Of course it's a typo, I'm sorry – user438666 May 31 '17 at 10:11
1 Answers
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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
$y(t)=(x(t)-4)^2$.
Your turn !
Fred
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