91Ó°ÊÓ

Find the center, foci, and vertices of each ellipse. Graph each equation. $$\frac{(x+4)^{2}}{9}+\frac{(y+2)^{2}}{4}=1$$

Parametric equations of four plane curves are given. Graph each of them, indicating the orientation. \(\begin{array}{ll}C_{1}: & x(t)=t, \quad y(t)=\sqrt{1-t^{2}} ; \quad-1 \leq t \leq 1 \\ C_{2}: & x(t)=\sin t, \quad y(t)=\cos t ; \quad 0 \leq t \leq 2 \pi \\\ C_{3}: & x(t)=\cos t, \quad y(t)=\sin t ; \quad 0 \leq t \leq 2 \pi \\\ C_{4}: & x(t)=\sqrt{1-t^{2}}, \quad y(t)=t ; \quad-1 \leq t \leq 1\end{array}\)

Find the vertex, focus, and directrix of each parabola. Graph the equation. \((x+4)^{2}=16(y+2)\)

Find an equation for the hyperbola described. Graph the equation. Center at (1,4)\(;\) focus at (-2,4)\(;\) vertex at (0,4)

Find the center, foci, and vertices of each ellipse. Graph each equation. $$(x+5)^{2}+4(y-4)^{2}=16$$

In Problems \(45-48\), use a graphing utility to graph the plane curve defined by the given parametric equations. \(x(t)=t \sin t, \quad y(t)=t \cos t, \quad t>0\)

Find the vertex, focus, and directrix of each parabola. Graph the equation. \((x-3)^{2}=-(y+1)\)

Use a graphing utility to graph the plane curve defined by the given parametric equations. \(x(t)=\sin t+\cos t, \quad y=\sin t-\cos t\)

Find the center, foci, and vertices of each ellipse. Graph each equation. $$9(x-3)^{2}+(y+2)^{2}=18$$

Find the center, foci, and vertices of each ellipse. Graph each equation. $$x^{2}+4 x+4 y^{2}-8 y+4=0$$