91Ó°ÊÓ

Eliminate the parameter and obtain the standard form of the rectangular equation. Hyperbola: \(x=h+a \sec \theta, y=k+b \tan \theta\)

Find the \(x\) - and \(y\) -intercepts of the graph of the circle. $$x^{2}+8 x+y^{2}+2 y+9=0$$

(a) find the standard form of the equation of the ellipse, (b) find the center, vertices, foci, and eccentricity of the ellipse, and (c) sketch the ellipse. Use a graphing utility to verify your graph. $$9 x^{2}+4 y^{2}-54 x+40 y+37=0$$

Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Eccentricity} & \text{Directrix} \\\ \text{Ellipse} &e=\frac{3}{4}&y=-4\end{array}$$

Use a graphing utility to graph the polar equation. Describe your viewing window. $$r=6-4 \sin \theta$$

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. 9 x^{2}-y^{2}+54 x+10 y+55=0

Plot the point given in rectangular coordinates and find two sets of polar coordinates for the point for \(\mathbf{0} \leq \boldsymbol{\theta}<\mathbf{2} \pi\) $$(3,-1)$$

Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Eccentricity} & \text{Directrix} \\\ \text{Hyperbola} &e=2&x=1\end{array}$$

Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (±1,0)\(;\) asymptotes: \(y=\pm 5 x\)

Use a graphing utility to graph the polar equation. Describe your viewing window. $$r=\frac{3}{\sin \theta-2 \cos \theta}$$