# Math 122 - Chapter 11 Study Guide

1. Convert polar coordinates into rectangular coordinates. Look at problems 11.1.1-2.
2. Know how the eccentricity determines the conic section. Three parts.
3. Transform the polar equation into rectangular coordinates. Look at problems 11.1.9-10.
4. Express the given rectangular equation in polar form. Look at problems 11.1.11-12.
5. Identify each conic section or degenerate case by inspection. Nine parts. Look at the College Algebra lecture notes and problem 11.4.73.
6. Find dy/dx at the given point without eliminating the parameter. Look at problems 11.2.5-10.
7. Find the area of the region described in polar form. Look at problems 11.3.5-22.
8. Sketch the curve in polar coordinates. Four parts. Look at problems 11.1.21-50.
9. 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.
10. Calculate the arclength of a polar curve. Hint: know your half-angle identities in reverse. Look at problems 11.2.39-44.
11. Sketch the ellipse and label the foci, vertices, and endpoints of the minor axis. Look at problems 11.4.9-14.
12. Sketch the hyperbola, and label the vertices, foci, and asymptotes. Look at problems 11.4.15-20.
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. 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 first day of the exam.
• Here are some instructions on using Derive to answer the last question on the take home exam.

## Points per problem

 # 1 2 3 4 5 6 7 8 9 10 11 12 13 Take Home Total Pts 3 3 4 4 9 5 5 8 4 5 5 5 5 35 100