## Multivariable Calculus, 7th Edition

a) As t increases, x increases and y decreases. b) $y=1-x^{2}$ $x \geq 0$
a) $x=\sqrt t$ $y=1-t$ When, t=-2 x=undefined y=3 t=-1 x=undefined y=2 t=0 x=0 y=1 t=1 x= 1 y=0 t=2 $x=\sqrt 2$ y=-1 t=3 $x=\sqrt 3$ y=-2 b) $x=\sqrt t$ $x^{2}=t$ $y=1-t$ $y=1-x^{2}$ From part a), we can infer that $x \geq 0$ because x is undefined at any negative t values.