Name:    Chapter 10 Pre 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 and determine the coordinates of the focus.
 a. b. c. d. e.

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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.

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.

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

11.

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

12.

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

13.

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

14.

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

15.

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)

16.

Find the standard form of the equation of the ellipse with vertices and eccentricity .
 a. b. c. d. e.

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.
 vertices: (0, –1), (10, –1) asymptotes:
 a. b. c. d. e.

20.

A small submarine is in a narrow underwater canyon 30 feet above the bottom searching for two sunken ships that are known to be 500 feet apart on the canyon floor. The sonar indicates that one of the wrecks is on the bottom in front of the sub, 475 feet from the nose of the sub, and the other wreck is on the bottom directly behind the sub, 75 feet from the nose. The difference in the distance from the wrecks to the sub is constant on a hyperbola having the wrecks as foci.

Assume the two wrecks are positioned on a rectangular coordinate system at points with coordinates (-250, 0) and (250, 0) as shown in the figure. Find the x-coordinate of the position of the submarine. (Round to the nearest whole number, if necessary.)

 a. x = 204 b. x = 200 c. x = 38,400 d. x = 250 e. x = 150