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39 votes
Which rectangular equation represents the parametric equations x = t²-4 and y = 2t?

Oy = 2(x² + 4)
* y = 2(x² - 4)
Oy = 2√x+4
O y = 2√√x-4

Which rectangular equation represents the parametric equations x = t²-4 and y = 2t-example-1
User Mite Mitreski
by
2.5k points

2 Answers

28 votes
28 votes

Answer:

c

Explanation:

User Merqlove
by
3.1k points
14 votes
14 votes

Answer:


\displaystyle{y=2√(x+4)}

Explanation:

We are given parametric equations of:


\displaystyle{x=t^2-4} and
\displaystyle{y=2t}

Isolate t-variable in
\displaystyle{x=t^2-4} first by adding both sides by 4:


\displaystyle{x+4=t^2-4+4}\\\\\displaystyle{x+4=t^2}

Square root both sides then write plus-minus:


\displaystyle{√(x+4)=√(t^2)}\\\\\displaystyle{t=\pm √(x+4)}

Since the choice determines y-term as a function and only positive t-value exists, substitute only
\displaystyle{t=√(x+4)} in
\displaystyle{y=2t}.

Therefore, the answer is
\displaystyle{y=2√(x+4)}

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