91Ó°ÊÓ

For each plane curve, find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=e^{t}, y=e^{-t}, \text { for } t \text { in }(-\infty, \infty)$$

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$x^{2}=25+y^{2}$$

Find an equation for each ellipse. \(x\) -intercepts \((\pm 3,0) ; y\) -intercepts \((0, \pm 6)\)

For each plane curve, find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=e^{2 t}, y=e^{t}, \text { for } t \text { in }(-\infty, \infty)$$

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$9 x^{2}+36 y^{2}=36$$

For each plane curve, find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=\frac{1}{\sqrt{t+2}}, y=\frac{t}{t+2}, \text { for } t \text { in }(-2, \infty)$$

Graph each circle by hand if possible. Give the domain and range. $$x^{2}+y^{2}=4$$

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$\frac{x^{2}}{4}+\frac{y^{2}}{4}=-1$$

Find an equation for each ellipse. Endpoints of major axis at ( \(6,0\) ) and ( \(-6,0\) ); \(c=4\)

For each plane curve, find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=\frac{t}{t-1}, y=\frac{1}{\sqrt{t-1}}, \text { for } t \text { in }(1, \infty)$$