Math 116: Study Guide - Chapter 8

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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. Know the relationship between the distances between the focus and a point on a parabola and the directrix and the same point.
3. Know the relationship between the distances between the foci and a point on an ellipse.
4. Know the relationship between the distances between the foci and a point on a hyperbola.
5. Know the Pythagorean relationship for an ellipse.
6. Know the Pythagorean relationship for a hyperbola.
7. Match the term with the definition. Nine parts.
8. Know the standard form for a parabola with vertex at (h,k).
9. Know the standard form for an ellipse with vertex at (h,k).
10. Know the standard form for a hyperbola with vertex at (h,k).
11. Label the vertex, directrix, and focus of a parabola.
12. Label the vertices, endpoints of the minor axis, and foci of an ellipse.
13. Label the vertices, endpoints of the conjugate axis, and foci of an ellipse.
14. Sketch the graph of the parametric equations.
15. Eliminate the parameter. Two parts.
16. Sketch the graph of a conic section in standard form.
17. Complete the square to put a conic into standard form and then sketch it.
18. Write the equation of the conic section shown. Three parts; a parabola, ellipse, and hyperbola (not necessarily in that order).
19. Application problem. Find the equation of a parabola. Then use the equation to find the coordinates of a point on the parabola.
20. Application problem. Find the equation of an ellipse.

Notes:

• No problems are directly from the text that I know of. If they are, they are unintentional.
• Problems 1 and 7 are matching.
• Problems 2-6 and 8-10 are multiple choice.
• The handout on conics has much of the information you need for the multiple choice questions, labeling, etc., on it. A PDF version is available in case you didn't get one in class.