Name: Class: Date: Chapter 10 Test Review Short Answer 1. Write an equation of a parabola with a vertex at the origin and a focus at ( 2, 0). 2. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5. 3. Use the graph to write an equation for the parabola. 4. Identify the vertex, focus, and directrix of the graph of y = 1 8 (x 2)2 + 5. 5. Identify the vertex, focus and the directrix of the graph of 8x 28y 124 = 0. 6. Write an equation of a circle with center ( 5, 8) and radius 2. 1
Name: 7. Write an equation in standard form for the circle. 8. Find the center and radius of the circle with equation ( x 5) 2 + Ê Á y + 6ˆ 2 = 9. 9. Graph ( x + 4) 2 + Ê Á y 7ˆ 2 = 49. 10. Write an equation in standard form of an ellipse that has a vertex at (5, 0), a co-vertex at (0, 3), and is centered at the origin. Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics. 11. a vertex at ( 5, 0) and a co vertex at (0, 4) 12. height of 4 units and width of 5 units 2
Name: 13. Find the foci of the ellipse with the equation 49 + y 2 64 = 1. Graph the ellipse. 14. Write an equation for the graph. Graph the conic section. 15. 4 9y 2 = 144 16. Find the foci of the graph 25 y 2 16 = 1. Draw the graph. 17. Find the equation of a hyperbola with a = 452 units and c = 765 units. Assume that the transverse axis is horizontal. 18. Write an equation of a hyperbola with vertices (3, 2) and ( 9, 2), and foci (7, 2) and ( 13, 2). 3
Name: 19. Write an equation of an ellipse with center (3, 4), horizontal major axis of length 16, and minor axis of length 10. 20. Write an equation for an ellipse with center (1, 3), vertices (1, 2) and (1, 8), and co vertices (4, 3) and ( 2, 3). Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci. 21. 4 + 7y 2 + 32x 56y + 148 = 0 22. y 2 4x + 6y + 29 = 0 23. 8 6y 2 + 48x 24y + 0 = 0 24. + y 2 + 8x 4y = 11 25. Find the center and radius of the circle with equation (x 1) 2 + (y + 1) 2 = 4. 26. A radio station has a broadcast area in the shape of a circle with equation + y 2 = 6, 400, where the constant represents square miles. a. Graph the equation and state the radius in miles. b. What is the area of the region in which the broadcast from the station can be picked up? 4
Name: Other 27. Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If the ellipse is placed on a large coordinate grid with its center at (0, 0), the equation 4624 + y 2 = 1 models the path of the track. 11236 The units are given in yards. How long is the major axis of the track? Explain how you found the distance. 5
Chapter 10 Test Review Answer Section SHORT ANSWER 1. x = 1 8 y 2 2. y = 1 20 3. y = 4 4. vertex (2, 5), focus (2, 7), directrix at y = 3 5. vertex (4, 5), focus(4, 2), directrix at y = 12 6. ( x + 5) + Ê Á y + 8ˆ = 4 7. ( x + 1) + Ê Á y + 3ˆ = 4 8. (5, 6); 3 9. 10. 11. 12. 25 + y 2 9 = 1 25 + y 2 16 = 1 6.25 + y 2 4 = 1 1
13. foci (0, ± 15) 14. 4 + y 2 16 = 1 15. 16. (± 41, 0) 17. 204, 304 y 2 380, 921 = 1 2
18. 19. 20. (x + 3) 2 36 ( x 3) 2 64 ( x 1) 2 9 + + Ê Á y + 2 ˆ 2 64 Ê Á y 4 ˆ 2 25 Ê Á y + 3 ˆ 2 25 = 1 = 1 = 1 21. ellipse with center ( 4, 4), foci at ( 4 ± 3, 4) 22. parabola; vertex (5, 3) 23. hyperbola with center ( 3, 2), foci at ( 3 ± 14, 2) 24. circle; center ( 4, 2); radius = 3 25. center (1, 1); radius 2 26. a. The radius of the circle is 80 miles. b. about 20,100 square miles OTHER 27. When the equation for an ellipse is in the standard form b + y 2 = 1, the major axis can be determined by the 2 a 2 greater value of the denominator. In this case, the greater denominator is with the y 2 term, so the ellipse has a vertical major axis. The distance from the center of the ellipse to a vertex is a. In this case, a = 11236 = 106. The length of the major axis of the track is twice a or 212 yards. 3