## 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 equation in polar form
7. Identify each conic section or degenerate case by inspection. Nine parts.
8. Sketch the curve in polar coordinates. Four parts
9. Find dy/dx and d2y/dx2 at the given point without eliminating the parameter.
10. Calculate the arclength of a polar curve
11. Find the area of the region described in polar form. Two parts.
12. Sketch the ellipse and label the foci, vertices, and endpoints of the minor axis.
13. Sketch the hyperbola, and label the vertices, foci, and asymptotes.
14. Rewrite the conic section in rectangular coordinates.

### Notes:

• Problems 3, 5, 6, and 8 - 14 are directly from the textbook
• There is a take home portion of the exam. The take home portion is worth 30 points and is due by 1:00 pm on Thursday, May 6.
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total Pts 6 4 3 3 3 4 9 8 4 4 8 5 5 4 70