219 2.2 Circles Concept Check Work each of the following. 47. Find the center-radius form of the equation of a circle with center 13, 22 and tangent to the x-axis. (Hint: A line tangent to a circle touches it at exactly one point.) 48. Find the equation of a circle with center at 1-4, 32, passing through the point 15, 82. Write it in center-radius form. 49. Find all points 1x, y2 with x = y that are 4 units from 11, 32. 50. Find all points satisfying x + y = 0 that are 8 units from 1-2, 32. 51. Find the coordinates of all points whose distance from 11, 02 is 210 and whose distance from 15, 42 is 210. Give the center and radius of the circle represented by each equation. See Examples 3 and 4. 27. x2 + y2 + 6x + 8y + 9 = 0 28. x2 + y2 + 8x - 6y + 16 = 0 29. x2 + y2 - 4x + 12y = -4 30. x2 + y2 - 12x + 10y = -25 31. 4x2 + 4y2 + 4x - 16y - 19 = 0 32. 9x2 + 9y2 + 12x - 18y - 23 = 0 33. 9x2 + 9y2 - 6x + 6y - 23 = 0 34. 4x2 + 4y2 + 4x - 4y - 7 = 0 Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. 35. x2 + y2 + 2x - 6y + 14 = 0 36. x2 + y2 + 4x - 8y + 32 = 0 37. x2 + y2 - 6x - 6y + 18 = 0 38. x2 + y2 + 4x + 4y + 8 = 0 39. x2 + y2 - 2x + 12y - 12 = 0 40. x2 + y2 + 8x - 18y - 24 = 0 41. x2 + y2 + 4x + 14y = -54 42. x2 + y2 - 10x - 16y = -105 Epicenter of an Earthquake Solve each problem. To visualize the situation, use graph paper and a compass to carefully graph each circle. See Example 6. 43. Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points 17, 42, 1-9, -42, and 1-3, 92, respectively. The epicenter of an earthquake is determined to be 5 units from X, 13 units from Y, and 10 units from Z. Where on the coordinate plane is the epicenter located? 44. Suppose that receiving stations P, Q, and R are located on a coordinate plane at the points 13, 12, 15, -42, and 1-1, 42, respectively. The epicenter of an earthquake is determined to be 25 units from P, 6 units from Q, and 2210 units from R. Where on the coordinate plane is the epicenter located? 45. The locations of three receiving stations and the distances to the epicenter of an earthquake are contained in the following three equations: 1x - 222 + 1y - 122 = 25, 1x + 222 + 1y - 222 = 16, and 1x - 122 + 1y + 2 2 = 9. Determine the location of the epicenter. 46. The locations of three receiving stations and the distances to the epicenter of an earthquake are contained in the following three equations: 1x - 222 + 1y - 422 = 25, 1x - 122 + 1y + 322 = 25, and 1x + 322 + 1y + 622 = 100. Determine the location of the epicenter.
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