## Math 122 - Chapter 12 Study Guide

- Know the tests for symmetry for rectangular and polar coordinates. Six parts.
- Definitions: Know the definitions of the conic sections. Four parts.
- Convert polar coordinates into rectangular coordinates
- Know how the eccentricity determines the conic section Three parts.
- Transform the polar equation into rectangular coordinates
- Express the given equation in polar form
- Identify each conic section or degenerate case by inspection. Nine parts.
- Sketch the curve in polar coordinates. Four parts
- Find dy/dx and d
^{2}y/dx^{2} at the given point without eliminating the parameter.
- Calculate the arclength of a polar curve
- Find the area of the region described in polar form. Two parts.
- Sketch the ellipse and label the foci, vertices, and endpoints of the minor axis.
- Sketch the hyperbola, and label the vertices, foci, and asymptotes.
- 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 |