91Ó°ÊÓ

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$\frac{(y+2)^{2}}{9}-\frac{(x+2)^{2}}{4}=1$$

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. $$x=2-3 \sin t, \quad y=-1-3 \cos t, \quad 0 \leq t \leq 2 \pi$$

Change the rectangular coordinates to polar coordinates with \(r>0\) and \(0 \leq \theta \leq 2 \pi\). (a) \((7,-7 \sqrt{3})\) (b) \((5,5)\)

Find the eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$r=\csc \theta(\csc \theta-\cot \theta)$$

Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$x^{2}+2 y^{2}+2 x-20 y+43=0$$

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. $$x=\cos t-2, \quad y=\sin t+3 ; \quad 0 \leq t \leq 2 \pi$$

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$\frac{(x-3)^{2}}{25}-\frac{(y-1)^{2}}{4}=1$$

Exer. \(1-12\) : Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$y^{2}-4 y-2 x-4=0$$

Change the rectangular coordinates to polar coordinates with \(r>0\) and \(0 \leq \theta \leq 2 \pi\). (a) \((-2 \sqrt{2},-2 \sqrt{2})\) (b) \((-4,4 \sqrt{3})\)

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$144 x^{2}-25 y^{2}+864 x-100 y-2404=0$$