#### Answer

$y=-x^{2}+1$,
See image:

#### Work Step by Step

a.
Build a table of coordinates (x,y)
$x=f(t)=\sqrt{t},\quad \qquad y=g(t)=1-t$
Plot the points and join with a smooth curve.
Taking the initial t to be the first point in the table, track the direction in which the points "travel" as t increases.
b.
From $ x=x=\sqrt{t}, \quad x \geq 0, t\geq 0, t=x^{2}$
$x^{2}=\sin^{2}t$
Substituting t into the other equation, we get
$y=1-t$
$y=-x^{2}+1$,
a concave down parabola wing.