# Math 122 - Chapter 11 Study Guide

- Convert polar coordinates into rectangular coordinates. Look at problems
11.1.1-2.
- Know how the eccentricity determines the conic section. Three parts.
- Transform the polar equation into rectangular coordinates. Look at problems
11.1.9-10.
- Express the given rectangular equation in polar form. Look at problems 11.1.11-12.
- Identify each conic section or degenerate case by inspection. Nine parts.
Look at the College Algebra
lecture notes and problem 11.4.73.
- Find dy/dx at the given point without eliminating the parameter. Look at
problems 11.2.5-10.
- Find the area of the region described in polar form. Look at problems 11.3.5-22.
- Sketch the curve in polar coordinates. Four parts. Look at problems 11.1.21-50.
- Rewrite the conic section in rectangular coordinates. There really isn't
any problem in the text I can point to for this. Just pretend it's a regular
polar to Cartesian conversion and complete the square to get it in standard
form.
- Calculate the arclength of a polar curve. Hint: know your half-angle identities
in reverse. Look at problems 11.2.39-44.
- Sketch the ellipse and label the foci, vertices, and endpoints of the minor
axis. Look at problems 11.4.9-14.
- Sketch the hyperbola, and label the vertices, foci, and asymptotes. Look
at problems 11.4.15-20.
- 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. Look at problems 11.6.1-4, 9-12.

## Notes

- The in-class part of the test is worth 65 points.
- There is a take home portion
of the exam. The take home portion is worth 35 points and
is due on the day of the exam.
- Handout on Conic Sections. This has all
of the information about conics in rectangular coordinates, but it is a fill-in-the-blank
activity for students to take notes.
- Summary sheet for conic sections in rectangular coordinates. This has just
the facts, but it's not fill-in-the-blank
- You will need WinPlot to generate the graphs for the last question on the
take home exam.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
Total |

Pts |
3 |
3 |
4 |
4 |
9 |
5 |
5 |
8 |
4 |
5 |
5 |
5 |
5 |
65 |