91Ó°ÊÓ

Find the center, vertices, foci, and eccentricity of the ellipse, and sketch its graph. Use a graphing utility to verify your graph. $$\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$$

Identify the type of conic represented by the polar equation and analyze its graph. Then use a graphing utility to graph the polar equation. $$r=\frac{-4}{-1+\cos \theta}$$

Use a graphing utility to graph the curve represented by the parametric equations. Use the graph and the Vertical Line Test to determine whether \(y\) is a function of \(x.\) $$\begin{aligned} &x=4+3 \cos \theta\\\ &y=-2+2 \sin \theta \end{aligned}$$

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(8.25,3.5)$$

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch its graph using the asymptotes as an aid. Use graphing utility to verify your graph \(\frac{(y+4)^{2}}{\frac{1}{9}}-\frac{(x+3)^{2}}{\frac{1}{4}}=1\).

Sketch the circle. Identify its center and radius. $$x^{2}-6 x+y^{2}+6 y+14=0$$

Use symmetry to sketch the graph of the polar equation. Use a graphing utility to verify your graph. $$r=3+6 \cos \theta$$

Find the center, vertices, foci, and eccentricity of the ellipse, and sketch its graph. Use a graphing utility to verify your graph. $$\frac{(x-4)^{2}}{16}+\frac{(y+1)^{2}}{25}=1$$

Find the standard form of the equation of the hyperbola, (b) find the center, vertices, foci, and asymptotes of the hyperbola, and (c) sketch the hyperbola. Use a graphing utility to verify your graph. \(4 x^{2}-9 y^{2}=36\)

Use a graphing utility to graph the curve represented by the parametric equations. Use the graph and the Vertical Line Test to determine whether \(y\) is a function of \(x.\) $$\begin{aligned} &x=4 \sec \theta\\\ &y=2 \tan \theta \end{aligned}$$