Practice section 1 of 6

Find the coordinates where $x=t^2$, $y=t+2$, $t\in\mathbb R$, meets the x- and y-axes.

Sketch (a) $x=t^2$, $y=2t$, $t\in\mathbb R$; (b) $x=\cos^2t$, $y=\sin^3t$, $0\le t\le\pi/2$.

For $x=at$, $y=a/(1+t^2)$, $t\in\mathbb R$, where $a>0$, find the y-axis intersection and any asymptotes. Sketch the curve.

For $x=1/\sqrt{t+1}$ and $y=t/(t+1)$, find a Cartesian equation and sketch the curve.

Find the Cartesian equation of $x=8\cos\theta$, $y=4\sin\theta$, $0\le\theta\le2\pi$.

For $x=t+1/t$, $y=t-1/t$, find a Cartesian equation and sketch the curve, showing axial intercepts and asymptotes.