Math 122 - Chapter 11 Study Guide

1. Convert polar coordinates into rectangular coordinates
2. Know how the eccentricity determines the conic section Three parts.
3. Transform the polar equation into rectangular coordinates
4. Express the given rectangular equation in polar form
5. Identify each conic section or degenerate case by inspection. Nine parts.
6. Find dy/dx at the given point without eliminating the parameter.
7. Find the area of the region described in polar form.
8. Sketch the curve in polar coordinates. Four parts
9. Rewrite the conic section in rectangular coordinates.
10. Calculate the arclength of a polar curve. Hint: know your half-angle identities in reverse.
11. Sketch the ellipse and label the foci, vertices, and endpoints of the minor axis.
12. Sketch the hyperbola, and label the vertices, foci, and asymptotes.
13. For the conic section given in polar form, identify the eccentricity and the conic, describe the distance and relationship of the pole to the directrix, find the coordinates of the vertices (or vertex), and sketch the graph.

Notes:

• There is a take home portion of the exam. The take home portion is worth 35 points and is due on Thursday, December 5.