Answer
(a) See the graph.
(b)
$x+y^2=1$
Work Step by Step
(a) $x=sin^2t$ and $y=cos~t$ are periodic functions. The maximum value of $cos~t$ is $1$ and the minimum is $-1$. In these points $y=cos~t$ change the directions. That is, $x$ and $y$ move back and forth from $(0,-1)$ to $(0,1)$.
(b)
$y=cos~t$
$y^2=cos^2t$
$x=sin^2t$
$sin^2t+cos^2t=1$
$x+y^2=1$
