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. $$x^{2}-2 y^{2}=8$$

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

Exer. 9-12: Change the rectangular coordinates to polar coordinates with \(r>0\) and \(0 \leq \theta \leq 2 \pi\). (a) \((-1,1)\) (b) \((-2 \sqrt{3},-2)\)

Exer. 1-12: Find the eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$ r=\frac{6 \csc \theta}{2 \csc \theta+3} $$

\(x=2-3 \sin t, \quad y=-1-3 \cos t ; \quad 0 \leq t \leq 2 \pi\)

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

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$16 x^{2}-36 y^{2}=1$$

Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$ \frac{(x-3)^{2}}{16}+\frac{(y+4)^{2}}{9}=1 $$

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$y^{2}-16 x^{2}=1$$

Exer. 9-12: Change the rectangular coordinates to polar coordinates with \(r>0\) and \(0 \leq \theta \leq 2 \pi\). (a) \((3 \sqrt{3}, 3)\) (b) \((2,-2)\)