91Ó°ÊÓ

(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. $$36 x^{2}+9 y^{2}+48 x-36 y+43=0$$

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. (There are many correct answers.) $$(3 \sqrt{2}, 3 \sqrt{2})$$

Find the eccentricity of the ellipse. $$\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$$

Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Vertex or Vertices} \\\ \text{Parabola} &(5, \pi)\end{array}$$

Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (1,2),(3,2)\(;\) asymptotes: \(y=x, y=4-x\)

Use a graphing utility to graph the polar equation. Describe your viewing window. $$r=8 \sin \theta \cos ^{2} \theta$$

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. (There are many correct answers.) $$\left(\frac{5}{2}, \frac{4}{3}\right)$$

Find a set of parametric equations to represent the graph of the given rectangular equation using the parameters (a) \(t=x\) and (b) \(t=2-x.\) $$y=4 x-9$$

Find the eccentricity of the ellipse. $$\frac{x^{2}}{25}+\frac{y^{2}}{49}=1$$

Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (3,0),(3,-6) asymptotes: \(y=x-6, y=-x\)