## Multivariable Calculus, 7th Edition

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.
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.