# Math 116 - Chapter 7 Study Guide

1. Identify the conic section or degenerate case. Choices are no graph, point, line, parallel lines, intersecting lines, parabola, circle, ellipse, and hyperbola. Nine parts.
2. Sketch the graph of the conic section. The conic is in standard form.
3. Find the equation of the parabola with vertex at the origin. Look at problems 7.1.11-18.
4. Find the equation of the ellipse with center at the origin. Look at problems 7.1.43-47.
5. Find the equation of the hyperbola with center at the origin. Look at problems 7.1.61-66.
6. Find the vertex, focus, and directrix of the parabola. Do not graph. Look at problems 7.2.17-24.
7. Find the center, foci, and vertices of the ellipse. Do not graph. Look at problems 7.2.33-36.
8. Find the center, foci, and vertices of the hyperbola. Also give the equations of the asymptotes. Do not graph. Look at problems 7.2.51-54.
9. Identify the conic section and write the equation based on the graph. If a parabola, give the focal length; if an ellipse, give the center; if a hyperbola, give the center. Look at problems 7.1.21-24, 39-42, and 67-68. Also look at problems 7.2.25-26, 41-42, and 61-62.
10. Same instructions as #9.
11. Same instructions as #9.
12. Complete the square to put a conic into standard form. Identify the type of conic, coordinates of the center (vertex for a parabola), and the change in x and change in y (for a hyperbola or ellipse) or focal length (for a parabola). Sketch the graph of the conic. Look at problems 7.2.37-40, 55-60.
13. Sketch the graph of the conic section. The conic is in standard form. Identify the type of conic, coordinates of the center (vertex for a parbola), and the change in x and change in y (for a hyperbola or ellipse) or focal length (for a parabola). Look at problems 8.2.33-36, 51-54.
14. Use your calculator to sketch the graph of the parametric equations. Indicate the direction of increasing t. Be aware of how to restrict the graph on the calculator to a certain interval for t. Look at problems 7.3.25-28.
15. Eliminate the parameter and solve for y. Then sketch the graph. Indicate the direction of increasing t. Be sure to include any restrictions that are necessary. Two parts. Look at problems 7.3.9-24.

## Notes:

• Problem 1 is matching.
• There is a take-home portion of the exam worth 18 points. It is due the day of the in-class exam.
• The in-class portion of the exam is worth 82 points.
• The take-home portion has two web pages to help you complete the problems. Click on the links below to save typing in the address provided on your test. You will need the username and password given to you at the beginning of the semester to gain access to these pages.
• The LORAN-C problem on the take home test can be difficult if you don't carefully read the instructions.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 9 4 5 5 5 5 5 5 5 5 5 7 5 4 8 82