91Ó°ÊÓ

Change the polar coordinates to rectangular coordinates. (a) \((5,5 \pi / 6)\) (b) \((-6,7 \pi / 3)\)

Find the vertices, the focl, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$\frac{x^{2}}{49}-\frac{y^{2}}{16}=1$$

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. $$x=t^{3}+1, \quad y=t^{3}-1 ; \quad-2 \leq t \leq 2$$

Find the vertices, the focl, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$x^{2}-\frac{y^{2}}{24}=1$$

Find the vertices and foct of the ellipse. Sketch Its graph, showing the foci. $$4 x^{2}+y^{2}=16$$

Change the polar coordinates to rectangular coordinates. (a) \((8,-2 \pi / 3)\) (b) \((-3,5 \pi / 3)\)

Find the eccentricity, and classify the conle. Sketch the graph, and label the vertices. $$r=\frac{3}{2+2 \cos \theta}$$

Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$(x+2)^{2}=-8(y-1)$$

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. \(x=4 t^{2}-5, \quad y=2 t+3\) \(t\) in \(\mathrm{R}\)

Find the vertices, the focl, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$y^{2}-\frac{x^{2}}{15}=1$$