Answer
$x^{2}+y^{2}=1,\qquad y\geq 0,\quad -1 \leq x\leq 0 $
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Work Step by Step
From the parametric equation for x,
$-1 \leq x\leq 0 $
Substituting into the parametric equation for y,
$y=\sqrt{1-x^{2}},\quad -1 \leq x\leq 0 $
Squaring gives
$y^{2}=1-x^{2},\qquad y\geq 0,\quad -1 \leq x\leq 0 $
$x^{2}+y^{2}=1,\qquad y\geq 0,\quad -1 \leq x\leq 0 $
This is the top left quarter of a circle centered at the origin, radius =1.
To graph, create a function value table using values for t, in ascending order of t, calculating the x- and y-coordinates of points on the graph.
Plot and join the points obtained with a smooth curve, noting the direction in which t increases.
