91Ó°ÊÓ

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

Find the vertex, focus, and directrix of each parabola. Graph the equation. \(y^{2}=8 x\)

Find a polar equation for each conic. For each, a focus is at the pole. \(e=\frac{2}{3} ;\) directrix is parallel to the polar axis, 3 units above the pole.

Find parametric equations for an object that moves along the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) with the motion described. The motion begins at \((0,3),\) is counterclockwise, and requires 1 second for a complete revolution.

Find parametric equations for an object that moves along the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) with the motion described. The motion begins at \((0,3),\) is clockwise, and requires 1 second for a complete revolution.

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

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

Find a polar equation for each conic. For each, a focus is at the pole. \(e=5 ;\) directrix is perpendicular to the polar axis, 5 units to the right of the pole.

Find the center, foci, and vertices of each ellipse. Graph each equation. $$\frac{(x-3)^{2}}{4}+\frac{(y+1)^{2}}{9}=1$$

In Problems 43 and \(44,\) parametric equations of four plane curves are given. Graph each of them, indicating the orientation. \(\begin{array}{ll}C_{1}: & x(t)=t, \quad y(t)=t^{2} ; \quad-4 \leq t \leq 4 \\\ C_{2}: & x(t)=\cos t, \quad y(t)=1-\sin ^{2} t ; \quad 0 \leq t \leq \pi \\\ C_{3}: & x(t)=e^{t}, \quad y(t)=e^{2 t} ; \quad 0 \leq t \leq \ln 4 \\\ C_{4}: & x(t)=\sqrt{t}, \quad y(t)=t ; \quad 0 \leq t \leq 16\end{array}\)