# Math 122 - Chapter 11 Study Guide

1. Convert polar coordinates into rectangular coordinates. Look at problems 11.1.3-4.
2. Convert rectangular coordinates into polar coordinates. Look at problems 11.1.7-8.
3. Know how the eccentricity determines the conic section. Three parts.
4. Transform the polar equation into rectangular coordinates. Look at problems 11.1.9-10.
5. Express the given rectangular equation in polar form. Look at problems 11.1.11-12.
6. Identify each conic section or degenerate case by inspection. Nine parts. Look at the College Algebra lecture notes.
7. Find dy/dx at the given point without eliminating the parameter. Look at problems 11.2.5-10.
8. Calculate the arclength of a polar curve. Look at problems 11.2.39-44.
9. Find the area of the region described in polar form. Look at problems 11.3.3-20.
10. Sketch the curve in polar coordinates. Four parts. Look at problems 11.1.21-50.
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.
14. Find a polar equation for the conic section that is described. Look at problems 11.6.5-8, 13-14.

## Notes

• The in-class part of the test is worth 70 points.
• There is a take home portion of the exam. The take home portion is worth 30 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.
• There is a page to help with the LORAN-C problem on the take home.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 3 3 3 5 5 9 5 5 5 8 5 5 5 4 70