Question

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

Answer 1

c

Explanation:

Answer 2

`\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)}`