91Ó°ÊÓ

Sketch the graph of the following parabolas. Specify the location of the focus and the equation of the directrix. Use a graphing utility to check your work. $$8 y=-3 x^{2}$$

Express the following polar coordinates in Cartesian coordinates. $$\left(1,-\frac{\pi}{3}\right)$$

Eliminate the parameter to find a description of the following circles or circular arcs in terms of \(x\) and \(y .\) Give the center and radius, and indicate the positive orientation. $$x=\sqrt{t}+4, y=3 \sqrt{t} ; 0 \leq t \leq 16$$

Find the points at which the following polar curves have a horizontal or a vertical tangent line. $$r=3+6 \sin \theta$$

Sketch the graph of the following parabolas. Specify the location of the focus and the equation of the directrix. Use a graphing utility to check your work. $$12 x=5 y^{2}$$

Eliminate the parameter to find a description of the following circles or circular arcs in terms of \(x\) and \(y .\) Give the center and radius, and indicate the positive orientation. $$x=3 \cos t, y=3 \sin t ; 0 \leq t \leq \pi / 2$$

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola that opens to the right with directrix \(x=-4\)

Find the points at which the following polar curves have a horizontal or a vertical tangent line. $$r=1-\sin \theta$$

Express the following polar coordinates in Cartesian coordinates. $$\left(-4, \frac{3 \pi}{4}\right)$$

Eliminate the parameter to find a description of the following circles or circular arcs in terms of \(x\) and \(y .\) Give the center and radius, and indicate the positive orientation. $$x=\cos t, y=1+\sin t ; 0 \leq t \leq 2 \pi$$