## 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. Write the standard form equations of a parabola, ellipse, and hyperbola with vertex (parabola) or center (ellipse and hyperbola) at the point (h,k). Know both the vertical and horizontal forms.
3. A sketch of a parabola is given. Identify the vertex, focus, and directrix. You may have to draw these on the parabola. Then, label the distance from the focus to a point on the parabola and the distance from the directrix to the same point on the parabola. Know the relationship between these two distances.
4. A sketch of an ellipse is given. Label the center, vertices, foci, and endpoints of the minor axis. Label the distances a, b, and c on the graph (arrows identifying the distances are given) and give the Pythagorean relationship between a, b, and c. Label the distances from the foci to a point on the ellipse and know the relationship between the distances.
5. A sketch of a hyperbola is given. Label the center, vertices, foci, and endpoints of the conjugate axis. Label the distances a, b, and c on the graph (arrows identifying the distances are given) and give the Pythagorean relationship between a, b, and c. Label the distances from the foci to a point on the hyperbola and know the relationship between the distances.
6. Sketch the graph of the parametric equations. Make sure your calculator is in Radian mode.
7. Eliminate the parameter. Two parts.
8. Application problem. Find the equation of an ellipse.
9. Sketch the graph of the conic sections. One parabola, one ellipse, one hyperbola. Two are in standard form. You need to complete the square on the other, and then graph it.

### Notes:

• The test may change. I quickly created this test from memory. I forgot to bring the textbook home with me when I made it up, so it is unlikely that any of the questions are directly from the text.