Name:    Chapter 10 Post Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin.
directrix:  x = 1
 a. x2 = –4y b. y2 = –4x c. x2 = 4y d. x2 = y e. y2 = x

2.

Find the vertex and focus of the parabola.
 a. vertex:      focus: b. vertex:      focus: c. vertex: (0, 0)     focus: d. vertex: (0, 0)     focus: e. vertex: (0, 0)     focus:

3.

Find the vertex and directrix of the parabola.
 a. vertex:           directrix: b. vertex:           directrix: c. vertex:           directrix: d. vertex:           directrix: e. vertex:           directrix:

4.

Give the standard form of the equation of the parabola with the given characteristics.
vertex: (–3, 1)          focus: (–1, 1)
 a. b. c. d. e.

5.

As a speeding train crosses a trestle over a deep gorge, a child drops his toy plane from the window. The path of the toy plane is modeled by , where y is the height above the floor of the gorge and distances are measured in feet. How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide; it "drops like a rock."]
 a. 900 ft b. 120 ft c. 30 ft d. 11 ft e. 7.5 ft

6.

An elliptical stained-glass insert is to be fitted in a

rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.
 a. b. c. d. e.

7.

Find the standard form of the equation of the ellipse with the following characteristics.
 foci: major axis of length: 20
 a. b. c. d. e.

8.

Find the standard form of the equation of the ellipse with the following characteristics.
foci:           major axis of length: 12
 a. b. c. d. e.

9.

Find the center and vertices of the ellipse.
 a. center: (7, 0)          vertices: (0, –2), (0, 2) b. center: (7, 2)          vertices: (–7, –2), (7, 2) c. center: (0, 0)          vertices: (0, –7), (0, 7) d. center: (0, 0)          vertices: (–7, 0), (7, 0) e. center: (0, 0)          vertices: (–2, 0), (2, 0)

10.

Identify the conic by writing the equation in standard form.
 a. ; ellipse b. ; circle c. ; circle d. ; circle e. ; ellipse

11.

Find the center and vertices of the ellipse.
 a. center:           vertices: b. center:           vertices: c. center:           vertices: d. center:           vertices: e. center:           vertices:

12.

Find the center and vertices of the ellipse.

= 0
 a. center: (3, –8)            vertices: (0, –8), (6, –8) b. center: (8, –3)                vertices: (5, –3), (11, –3) c. center: (–8, 3)            vertices: (–11, 3), (–5, 3) d. center: (–8, 3)            vertices: (–9, 3), (–7, 3) e. center: (8, –3)              vertices: (7, –3), (9, –3)

13.

Find the vertices and asymptotes of the hyperbola.
 a. vertices:           asymptote: b. vertices:           asymptote: c. vertices:           asymptote: d. vertices:           asymptote: e. vertices:           asymptote:

14.

Find the vertices and asymptotes of the hyperbola.
 a. vertices:           asymptote: b. vertices:           asymptote: c. vertices:           asymptote: d. vertices:           asymptote: e. vertices:           asymptote:

15.

Find the center and foci of the hyperbola.
 a. center: (1, 4), foci: (1, –4), (1, 12) b. center: (–1, –4), foci: (–1, –12), (–1, 4) c. center: (4, 1), foci: (4, –7), (4, 9) d. center: (–4, –1), foci: (–12, –1), (4, –1) e. center: (–1, –4), foci: (–9, –4), (7, –4)

16.

Find the center and vertices of the hyperbola.
 a. center: (1,–5), vertices: (–4, –5), (6, –5) b. center: (–5, 1), vertices: (–10, 1), (0, 1) c. center: (–1, 5), vertices: (–1, 0), (–1, 10) d. center: (–1, 5), vertices: (–6, 5), (4,5) e. center: (1, –5), vertices: (1, –10), (1, 0)

17.

Find the standard form of the equation of the hyperbola with the given characteristics.
vertices:           foci:
 a. b. c. d. e.

18.

Find the standard form of the equation of the hyperbola with the given characteristics.
 vertices: (–2, –4), (–2, 6) foci: (–2, –5), (–2, 7)
 a. b. c. d. e.

19.

Find the standard form of the equation of the hyperbola with the given characteristics.
foci:           asymptotes:
 a. b. c. d. e.

20.

A pinball machine is designed so that a bumper on one side is hyperbolic in shape. If a pinball is directed at its focus, the ball will be reflected to a 10,000 point bonus pocket positioned at the other focus (see figure). If the focus of the bumper has coordinates (8, 0), and the vertex of the bumper is (6, 0), find the standard form of the equation that models the shape of the bumper.
 a. b. c. d. e.