91Ó°ÊÓ

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=t^{2}-1, \quad y=\frac{t}{2}$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=\frac{1}{\sqrt{t+1}}, \quad y=\frac{t}{1+t}, t>-1$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=4 \cos \theta, y=3 \sin \theta, t \in(0,2 \pi]$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=\cosh t, \quad y=\sinh t$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=2 t-3, \quad y=6 t-7$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=t^{2}, \quad y=t^{3}$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=1+\cos t, \quad y=3-\sin t$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=\sqrt{t}, \quad y=2 t+4$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=\sec t, \quad y=\tan t, \pi \leq t<\frac{3 \pi}{2}$$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$x=2 \cosh t, \quad y=4 \sinh t$$