54 CHAPTER 1 Graphs In Problems 27–40, (a) find the center ( ) h k , and radius r of each circle; (b) graph each circle; (c) find the intercepts, if any. 27. + = x y 4 2 2 28. ( ) + − = x y 1 1 2 2 29. ( ) − + = x y 2 3 2 8 2 2 30. ( ) ( ) + + − = x y 3 1 3 1 6 2 2 31. + − − − = x y x y 2 4 4 0 2 2 32. + + + − = x y x y 4 2 20 0 2 2 33. + + − − = x y x y 4 4 1 0 2 2 34. + − + + = x y x y 6 2 9 0 2 2 35. + − + + = x y x y2 1 0 2 2 39. + + = x x y 2 8 2 0 2 2 36. + + + − = x y x y 1 2 0 2 2 37. + − + − = x y x y 2 2 12 8 24 0 2 2 38. + + + = x y x 2 2 8 7 0 2 2 40. + − = x y y 3 3 12 0 2 2 In Problems 41–46, find the standard form of the equation of each circle. 41. Center at the origin and containing the point ( ) −2, 3 42. Center ( ) 1, 0 and containing the point ( ) −3, 2 43. With endpoints of a diameter at ( ) 1, 4 and ( ) −3, 2 44. With endpoints of a diameter at ( ) 4, 3 and ( ) 0, 1 45. Center ( ) − 2, 4 and circumference π 16 46. Center ( ) −5, 6 and area π 49 In Problems 47–50, match each graph with the correct equation. (a) ( ) ( ) − + + = x y 3 3 9 2 2 (b) ( ) ( ) + + − = x y 1 2 4 2 2 (c) ( ) ( ) − + + = x y 1 2 4 2 2 (d) ( ) ( ) + + − = x y 3 3 9 2 2 47. 48. 49. 50. 51. Find an equation of the line containing the centers of the two circles ( ) ( ) − + + = x y 4 2 25 2 2 and ( ) ( ) + + − = x y 1 5 16 2 2 52. Find an equation of the line containing the centers of the two circles + − + + = x y x y 4 6 4 0 2 2 and + + + + = x y x y 6 4 9 0 2 2 53. If a circle of radius 2 rolls along the x-axis in quadrants I and II, what is an equation for the path of the center of the circle? 54. A circle of radius 7 rolls along the y-axis in quadrants I and IV. Find an equation for the path of the center of the circle. 55. Find the area of the square in the figure. x2 1 y2 5 9 y x 56. Find the area of the blue shaded region in the figure, assuming the quadrilateral inside the circle is a square. x2 1 y2 5 36 y x 57. Ferris Wheel The original Ferris wheel was built in 1893 by Pittsburgh, Pennsylvania bridge builder George W. Ferris. The Ferris wheel was originally built for the 1893 World’s Fair in Chicago, but it was also later reconstructed for the 1904 World’s Fair in St. Louis. It had a maximum height of 264 feet and a wheel diameter of 250 feet. Find an equation for the wheel if the center of the wheel is on the y-axis. Source: guinnessworldrecords.com 58. Ferris Wheel The High Roller observation wheel in Las Vegas has a maximum height of 550 feet and a diameter of 520 feet, with one full rotation taking approximately 30 minutes. Find an equation for the wheel if the center of the wheel is on the y-axis. Source: Las Vegas Review Journal Applications and Extensions Credit: Aneese/Shutterstock
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