Math 122 - Chapter 12 Study Guide

1. Know the tests for symmetry for rectangular and polar coordinates. Six parts.
2. Definitions: Know the definitions of the conic sections. Four parts.
3. Convert polar coordinates into rectangular coordinates
4. Know how the eccentricity determines the conic section Three parts.
5. Transform the polar equation into rectangular coordinates
6. Express the given rectangular equation in polar form
7. Identify each conic section or degenerate case by inspection. Nine parts.
8. Find dy/dx at the given point without eliminating the parameter.
9. Sketch the curve in polar coordinates. Four parts
10. Rewrite the conic section in rectangular coordinates.
11. Calculate the arclength of a polar curve
12. Find the area of the region described in polar form. Two parts.
13. Sketch the ellipse and label the foci, vertices, and endpoints of the minor axis.
14. Sketch the hyperbola, and label the vertices, foci, and asymptotes.

Notes:

• There is a take home portion of the exam. The take home portion is worth 35 points and is due by 5:00 pm on Thursday, December 7.
• Check here for more information on the Loran-C problem on the take home.