Answer
a)
$\frac{x^{2}}{2}-\frac{y^{2}}{2}=1$
$x \geq \sqrt 2$
$y \geq 0$
b)
As t increases, x also increases, so the arrow should be pointing in the direction that x increases in.
Work Step by Step
a)
Given:
$x=\sqrt (t+1)$
Isolate t:
$x^{2}=t+1$
$x^{2}-1=t$
Isolate t in the second equation:
$y=\sqrt (t-1)$
$y^{2}=t-1$
$y^{2}+1=t$
Put the two equations together:
$x^{2}-1=y^{2}+1$
$x^{2}-y^{2}=2$
$\frac{x^{2}}{2}-\frac{y^{2}}{2}=1$
Domain:
$x \geq \sqrt 2$
Range:
$y \geq 0$
b)
We know,
$\frac{x^{2}}{2}-\frac{y^{2}}{2}=1$
$x \geq \sqrt 2$
$y \geq 0$
Now graph. It should be in the first quadrant.
As t increases, so does x.
