9.1, 9.3 – 9.4 Quiz Review Algebra 2 CP Find the center and radius. Then graph the circle. 1. y 2 x 2 16 2. x 2 y 2 20 4. 5x 2 5 y 2 80 5. x 2 2 y 2 Name________________ Date_________________ 3. 25 6. x 32 y 22 x 12 y 52 9 22 Write the equation of the circle that satisfies the given information. 7. Center (0, 0); r = 7 8. Center (0, 0); r = 3 3 9. Center (6, -1); r = 9 10. Center (0, 0); r = 17 13. Center (0, 0) and the point on the circle (5, 1) 11. Center (0, 4); r = 2 6 12. Center (-3, -5); r = 3 14. Center (0, 0) and the point on the circle (-3, 4) 15. Center (0, 0) and the point on the circle (-6, -2) 16. Center (0, 0) and the point on the circle (5, -8) 17. Center (2, -1) and the point on the circle (3, 6) 18. Center (-5, -2) and the point on the circle (-3, 4) 19. Center (6, -8) and the point on the circle (4, -2) 20. Center (1, 5) and the point on the circle (-2, 3) Identify the vertices, co-vertices, and foci. Then, graph the ellipse. x2 y2 x2 y2 21. 22. 1 1 9 16 36 25 23. x2 y2 1 17 24. 16 x 2 4 y 2 64 x2 y2 25. 1 25 49 27. 29. x2 y2 1 15 9 x 12 9 y2 1 16 26. x 2 49 y 2 49 28. 36 x 2 4 y 2 144 x 2 y 2 1 25 4 2 30. 31. 33. x 22 y 12 16 x 32 25 9 1 y2 1 32. x 32 y 22 1 34. x 12 y 32 1 4 16 36 Find the coordinates of the foci of the ellipse centered at the origin with the given information. 35. Vertices: (0, -5) (0, 5); 36. Vertices: (-9, 0) (9, 0); Co-vertices: (-4, 0) (4, 0) Co-vertices: (0, -1) (0, 1) 37. Vertices: (-13, 0) (13, 0); Co-vertices: (0, -2) (0, 2) 38. Vertices:(0, -12) (0, 12); Co-vertices: (-3, 0) (3, 0) Write an equation that satisfies the given information. 39. Center (0, 0); Vertex (0, -6); 40. Center (0, 0); Vertex (8, 0); Co-Vertex (3, 0) Co-Vertex (0, 4) 41. Center (0, 0); Vertex (-6, 0); Focus (3, 0) 42. Center (0, 0); Vertex (0, -6); Focus (0, 4) 43. Center (0, 0); Vertex (4, 0); Co-Vertex (0, 2) 44. Center (0, 0); Vertex (0, -3); Co-Vertex (2, 0) 45. Center (0, 0); Vertex (3, 0); Focus (1, 0) 46. Center (0, 0); Vertex (0, -10); Focus (0, 7) 47. Center (-2, 6); Vertex (-2, 10); Co-Vertex (0, 6) 48. Center (3, 6); Vertex (7, 6) Co-Vertex (3, 3) 49. Center (4, -3); Vertex (12, -3) Focus (10, -3) 50. Center (-1, -4); Vertex (-1, 1) Focus (-1, -2) 51. Vertices (-2, 5) (6, 5) Co-Vertices (2, 7) (2, 3) 52. Vertices (-3, 0) (-3, 6) Co-Vertices (-4, 3) (-2, 3) 53. Vertices (6, -1) (6, 5) Foci (6, 4) (6, 0) 54. Vertices (-1, 2) (3, 2) Foci (0, 2) (2, 2) Answers 1. C: (0, 0); r = 4 C: (0, 0); r = 2 5 2. 3. C: (-3, 2); r = 3 22 4. C: (0, 0); r = 4 5. C: (2, 0); r = 5 6. C: (-1, 5); r = 7. x2 + y2 = 49 8. x2 + y2 = 27 9. (x – 6)2 + (y + 1)2 = 81 10. x2 + y2 = 17 11. x2 + (y – 4)2 = 24 12. (x + 3)2 + (y + 5)2 = 9 13. x2 + y2 = 26 14. x2 + y2 = 25 15. x2 + y2 = 40 16. x2 + y2 = 89 17. (x – 2)2 + (y + 1)2 = 50 18. (x + 5)2 + (y + 2)2 = 40 19. (x – 6)2 + (y + 8)2 = 40 20. (x – 1)2 + (y – 5)2 = 13 21. V: (0, ± 4) CV: (± 3, 0) F: 0, 7 22. V: (±6, 0) CV: (0, ±5) F: 11 , 0 23. V: 17 , 0 CV: (0, ±1) F: (±4, 0) 25. V: (0, ±7) CV: (±5, 0) F: 0, 2 6 28. V: (0, ±6) CV: (±2, 0) F: 0, 4 2 26. V: (±7, 0) CV: (0, ±1) F: 4 3 , 0 24. V: (0, ± 4) CV: (± 2, 0) F: 0, 2 3 27. V: 15 , 0 CV: (0, ±3) F: 6 , 0 29. V: (1, 4) (1, -4) CV: (4, 0) (-2, 0) F: (1, 2.6) (1, -2.6) 30. V: (5, -2) (-5, -2) CV: (0, 0) (0, -4) F: (4.6, -2) (-4.6, -2) 31. V: (6, -1) (-2, -1) CV: (2, 2) (2, -4) F: (4.6, -1) (-0.6, -1) 32. V: (-3, 8) (-3, -4) CV: (-5, 2) (-1, 2) F: (-3, 7.7) (-3, -3.7) 33. V: (2, 0) (-8, 0) CV: (-3, 1) (-3, -1) F: (1.9, 0) (-7.9, 0) 34. V: (5, 3) (-3, 3) CV: (1, 4) (1, 2) F: (4.9, 3) (-2.9, 3) 35. Foci: (0, ±3) 37. Foci: 165 , 0 38. Foci: 0, 3 15 36. Foci: 4 5 , 0 39. x2 y2 1 9 36 40. x2 y2 1 64 16 x2 y2 1 16 4 44. x2 y2 1 4 9 41. x2 y2 1 36 27 42. x2 y2 1 20 36 43. 45. x2 y2 1 9 8 46. x2 y2 1 51 100 47. x 22 y 62 1 4 16 48. x 32 y 62 1 49. x 42 y 32 1 50. x 12 y 42 1 51. x 22 y 52 1 52. x 32 y 3 1 53. x 62 y 22 1 54. x 12 y 22 1 16 16 4 9 4 3 64 28 2 9 21 5 25 9