## Math 117 - Chapter 5 Study Guide

1. Find the vertex, focus, and directrix for a parabola. Then draw the graph. Look at problems 5.1.21-30.
2. Find the equation of the parabola satisfying the given conditions. Look at problems 5.1.15-20.
3. Find the center, vertices, and foci of an ellipse. Then draw the graph. Look at problems 5.2.33-38.
4. Find the equation of the ellipse satisfying the given conditions. Look at problems 5.2.27-32.
5. Find the center, vertices, and foci of a hyperbola. Then draw the graph. Look at problems 5.3.11-16.
6. Find the equation of the hyperbola satisfying the given conditions. Look at problems 5.3.7-10.
7. Solve the system of non-linear equations. Two parts. Look at problems 5.4.7-54.
8. Use the discriminant to determine whether the graph of the equation is an ellipse, a hyperbola, or a parabola. Look at problems 5.5.9-18.
9. Find the polar coordinates of the point. Express the angle in radians. Look at problems 5.6.15-22.
10. Convert the rectangular equation into a polar equation. Look at problems 5.6.39-48.
11. Convert the polar equation into a rectangular equation. Look at problems 5.6.49-58.
12. Graph the polar equation by plotting points. Then check your work using a grapher. Look at problems 5.6.59-62.
13. Find the polar equation of the conic with a focus at the pole and the given eccentricity and directrix. Look at problems 5.7.39-48.
14. Graph the plane curve given by the set or parametric equations and the restriction for the parameter. Then find the equivalent rectangular equation. Look at problems 5.8.1-20.

### Notes:

• Some of the problems are directly from the text.
• There is a take home portion of the exam. The take home portion is worth 30 points and will be due the class period after the in-class exam.
Points for each problem
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Tot. pts 5 5 5 5 5 5 8 4 3 5 5 5 5 5 70