91Ó°ÊÓ

Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. $$r=1 \text { and } r=\sqrt{2} \cos 2 \theta$$

In Exercises \(37-40,\) you found the intersection points of pairs of curves. Find the area of the entire region that lies within both of the following pairs of curves. $$r=3 \sin \theta \text { and } r=3 \cos \theta$$

Find a parametric description of the line segment from the point \(P\) to the point \(Q\). Solutions are not unique. $$P(0,0), Q(2,8)$$

Graph the following equations. Use a graphing utility to check your work and produce a final graph. \(r=1-\sin \theta\)

Sketch a graph of the following hyperbolas. Specify the coordinates of the vertices and foci, and find the equations of the asymptotes. Use a graphing utility to check your work. $$4 x^{2}-y^{2}=16$$

Graph the following equations. Use a graphing utility to check your work and produce a final graph. \(r=2-2 \sin \theta\)

Sketch a graph of the following hyperbolas. Specify the coordinates of the vertices and foci, and find the equations of the asymptotes. Use a graphing utility to check your work. $$25 y^{2}-4 x^{2}=100$$

Find a parametric description of the line segment from the point \(P\) to the point \(Q\). Solutions are not unique. $$P(1,3), Q(-2,6)$$

In Exercises \(37-40,\) you found the intersection points of pairs of curves. Find the area of the entire region that lies within both of the following pairs of curves. $$r=2+2 \sin \theta \text { and } r=2-2 \sin \theta$$

In Exercises \(37-40,\) you found the intersection points of pairs of curves. Find the area of the entire region that lies within both of the following pairs of curves. $$r=1+\sin \theta \text { and } r=1+\cos \theta$$