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. $$y^{2}-\frac{x^{2}}{15}=1$$

Exer. 1-12: Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$ (x-3)^{2}=\frac{1}{2}(y+1) $$

Exer. 1-12: Find the eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$ r=\frac{4}{\cos \theta-2} $$

Exer. 1-12: Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$ (y-2)^{2}=\frac{1}{4}(x-3) $$

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$y^{2}-4 x^{2}=16$$

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

Exer. 3-8: Change the polar coordinates to rectangular coordinates. $$ \left(6, \arctan \frac{3}{4}\right) $$

Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$ 10 y^{2}+x^{2}=5 $$

Exer. 1-12: Find the eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$ r=\frac{4 \sec \theta}{2 \sec \theta-1} $$

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