Answer
$x^{2}+y^{2}=1,\qquad y\geq 0, x\leq 0$
Work Step by Step
Substituting into the parametric equation for y,
$y=\sqrt{1-x^{2}},\quad x\in[-1,0]\ \ (x\leq 0)$
squaring,
$y^{2}=1-x^{2},\qquad y\geq 0$
$\fbox{$x^{2}+y^{2}=1$},\qquad y\geq 0, x\leq 0$
(the top left quarter of a circle centered at the origin, radius =1).
To graph, create a table using several values for t, and then calculate $(x(t), y(t)),$ plotting the points as you go. Join with a smooth curve, noting the direction in which $t$ increases.
