## Math 116: Study Guide - Chapter 8

- Identify the conic section or degenerate case. Choices are: no graph, point, line, parallel lines,
intersecting lines, parabola, circle, ellipse, and hyperbola. Nine parts.
- 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.
- 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.
- A sketch of an ellipse is given. Label the vertices, foci, and endpoints of the minor axis using
the letters a, b, and c (whichever is appropriate based on the definition of the ellipse). 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 (d
_{1} + d_{2} = 2a)
- A sketch of a hyperbola is given. Label the vertices, foci, and endpoints of the conjugate axis
using the letters a, b, and c (whichever is appropriate based on the definition of the hyperbola).
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 ( | d
_{1} - d_{2} | = 2a ).
- Sketch the graph of the parametric equations.
- Eliminate the parameter. Two parts.
- Application problem. Find the equation of an ellipse.
- 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.
- Write the equation of the conic section shown. Four parts, a circle, parabola, ellipse, and
hyperbola (not necessarily in that order).

### Notes:

- Few of the problems are directly from the textbook. The parametric equation ones are about
it.
- Since there are few problems, each will be worth a substantial amount.