45–60. Areas of regions Find the area of the following regions.


The region inside the lemniscate r² = 6 sin 2θ

13–30. Graphing conic sections Determine whether the following equations describe a parabola, an ellipse, or a hyperbola, and then sketch a graph of the curve. For each parabola, specify the location of the focus and the equation of the directrix; for each ellipse, label the coordinates of the vertices and foci, and find the lengths of the major and minor axes; for each hyperbola, label the coordinates of the vertices and foci, and find the equations of the asymptotes.

x²/9 + y²/4 = 1

Express the polar equation r=f(θ) in parametric form in Cartesian coordinates, where θ is the parameter.

37–52. Curves to parametric equations Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique.

The upper half of the parabola x=y ², originating at (0, 0)

25–30. Converting coordinates Express the following polar coordinates in Cartesian coordinates.

(2, 7π/4)

What is the polar equation of a circle of radius √(a²+b²) centered at (a, b)?

75–76. Graphs to polar equations Find a polar equation for each conic section. Assume one focus is at the origin.