You may use a graphing utility to plot any polar graphs.

1. Without graphing or writing in standard form, explain why the graph for the equation 2 4 + 4 2 8 4 = 0 must be an ellipse.

2. For the hyperbola given as 16 2 2 32 6 57 = 0. a. Find the center, vertices, and foci. b. Sketch the graph of the hyperbola, include asymptotes.

3. Consider the curve represented by the parametric equations = 2 cos() and = 1 + sin (). a. Find the corresponding, recognizable rectangular equation. b. Make a sketch of the graph of the parametric curve.