91Ó°ÊÓ

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. $$x=\cos t, y=1+\sin t ; 0 \leq t \leq 2 \pi$$

Express the following polar coordinates in Cartesian coordinates. $$(4,5 \pi)$$

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola that opens downward with directrix \(y=6\)

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

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the curve \(r=\sqrt{\cos \theta}\)

Express the following Cartesian coordinates in polar coordinates in at least two different ways. $$(2,2)$$

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. $$x=-7 \cos 2 t, y=-7 \sin 2 t ; 0 \leq t \leq \pi$$

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola with focus at (-4,0)

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. $$x=1-3 \sin 4 \pi t, y=2+3 \cos 4 \pi t ; 0 \leq t \leq \frac{1}{2}$$

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the right lobe of \(r=\sqrt{\cos 2 \theta}\)