91Ó°ÊÓ

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

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 eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$r=\frac{8 \csc \theta}{2 \csc \theta-5}$$

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

Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$\frac{(x+2)^{2}}{25}+\frac{(y-3)^{2}}{4}=1$$

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. $$x=2 \sin t, \quad y=3 \cos t, \quad 0 \leq t \leq 2 \pi$$

Exer. \(1-12\) : Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$x^{2}+20 y=10$$

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

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. $$x=2-3 \sin t, \quad y=-1-3 \cos t, \quad 0 \leq t \leq 2 \pi$$

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