91Ó°ÊÓ

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) \((2,-2)\)

Exer. 1-12: Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$ y^{2}+14 y+4 x+45=0 $$

Exer. 1-12: Find the eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$ r=\frac{8 \csc \theta}{2 \csc \theta-5} $$

Exer. 9-12: Change the rectangular coordinates to polar coordinates with \(r>0\) and \(0 \leq \theta \leq 2 \pi\). (a) \((7,-7 \sqrt{3})\) (b) \((5,5)\)

Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$ 4 x^{2}+9 y^{2}-32 x-36 y+64=0 $$

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. $$\frac{(y+2)^{2}}{9}-\frac{(x+2)^{2}}{4}=1$$

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

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