91Ó°ÊÓ

Use a graphing utility to graph the rotated conic. $$r=\frac{7}{1+\sin (\theta-\pi / 3)}$$

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 \(x.\) $$\begin{aligned} &x=t / 2\\\ &y=\ln \left(t^{2}+1\right) \end{aligned}$$

Plot the point given in rectangular coordinates and find two sets of polar coordinates for the point for \(\mathbf{0} \leq \boldsymbol{\theta}<\mathbf{2} \pi\) $$(-7,0)$$

Find the center, vertices, foci, and eccentricity of the ellipse, and sketch its graph. Use a graphing utility to verify your graph. $$\frac{(x+5)^{2}}{\frac{9}{4}}+(y-1)^{2}=1$$

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. \(6 y^{2}-3 x^{2}=24\)

Use a graphing utility to graph the rotated conic. $$r=\frac{4}{1-5 \cos (\theta+3 \pi / 4)}$$

Identify and sketch the graph of the polar equation. Identify any symmetry and zeros of \(r .\) Use a graphing utility to verify your results. $$r=-7 \sin 2 \theta$$

Sketch the circle. Identify its center and radius. $$x^{2}+2 x+y^{2}-35=0$$

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. \(3 x^{2}-2 y^{2}=18\)

Sketch the circle. Identify its center and radius. $$x^{2}+y^{2}+10 y+9=0$$