91Ó°ÊÓ

Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$x^{2}+20 y=10$$

Find the vertices and foct of the ellipse. Sketch Its graph, showing the foci. $$4 x^{2}+9 y^{2}-32 x-36 y+64=0$$

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

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

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

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. $$x=\cos 2 t, \quad y=\sin t ; \quad-\pi \leq t \leq \pi$$

Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$y^{2}-4 y-2 x-4=0$$

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

Find the vertices and foct of the ellipse. Sketch Its graph, showing the foci. $$x^{2}+2 y^{2}+2 x-20 y+43=0$$

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