Math 116: Study Guide - Chapter 8

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. A labeled figure of a parabola is given. Be able to identify the vertex, focus, directrix, and axis of symmetry. Know the relationship of the distance between a point and the focus to the distance between a point and the directrix. Given some coordinates (vertex or focus) and/or distances, find the equation of the parabola (two parts).
4. A labeled figure of an ellipse is given. Be able to identify the vertices, foci, endpoints of minor axis. Know the relationship of the distances between a point and the foci to the rest of the ellipse. Know the Pythagorean relationship for an ellipse. Given some coordinates (center, vertex, or focus) and/or distances, find the equation of the ellipse (two parts).
5. A labeled figure of a hyperbola is given. Be able to identify the vertices, foci, endpoints of conjugate axis. Know the relationship of the distances between a point and the foci to the rest of the hyperbola. Know the Pythagorean relationship for a hyperbola. Given some coordinates (center, vertex, or focus) and/or distances, find the equation of the hyperbola (two parts).
6. Match the term with the definition. Nine parts. Know the names of each of the parts of the conic sections.
7. Complete the square to put a conic into standard form and then sketch it.
8. Sketch the graph of the conic section. The conic is in standard form.
9. Sketch the graph of the parametric equations. Indicate the direction of increasing t.
10. Eliminate the parameter and sketch the graph. Indicate the direction of increasing t. Two parts.

Notes:

• No problems are directly from the text that I know of. If they are, they are unintentional.
• Problems 1 and 6 are matching.
• There is a take-home portion of the exam worth 20 points. It is due the class period after the in-class exam.
• The in-class portion of the exam is worth 80 points.
• The lamp problem on the take home test will involve measuring a diagram to get coordinates of points. Here is an enlarged diagram (full sheet, pdf) if you want a little more accuracy. Don't do too much rounding on the intermediate steps. A hint is to let the vertex be at (0,0). The problem is you don't know where the vertex is. Think about it and I'll give you some hints later.
• The Loran-C problem on the take home test can be difficult if you don't carefully read the instructions. Here are some steps to help, but I want you to try it on your own first. If you need additional practice maps, you can get them in pdf format.
 # 1 2 3 4 5 6 7 8 9 10 Total Pts 9 5 10 11 11 9 6 5 4 10 80