91Ó°ÊÓ

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

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the circle \(r=8 \sin \theta\)

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 Cartesian coordinates in polar coordinates in at least two different ways. \((1, \sqrt{3})\)

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola symmetric about the \(y\) -axis that passes through the point (2,-6)

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola symmetric about the \(x\) -axis that passes through the point (1,-4)

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. $$x=2 \sin t-3, y=2 \cos t+5 ; 0 \leq t \leq 2 \pi$$

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the cardioid \(r=4+4 \sin \theta\)

Express the following Cartesian coordinates in polar coordinates in at least two different ways. (-9,0)

Express the following Cartesian coordinates in polar coordinates in at least two different ways. \((-4,4 \sqrt{3})\)