999 10.1 Parabolas Give the focus, directrix, and axis of symmetry for each parabola. See Example 3. 23. x2 = 24y 24. x2 = 1 8 y 25. y = -4x2 26. y = - 1 9 x2 27. y2 = -4x 28. y2 = 16x 29. x = -32y2 30. x = -16y2 31. 1y - 322 = 121x - 12 32. 1y - 222 = 241x - 32 33. 1x - 722 = 161y + 52 34. 1x + 222 = 201y - 22 Write an equation for each parabola with vertex at the origin. See Example 4. 35. focus 15, 02 36. focus A -1 2, 0B 37. directrix y = -1 4 38. directrix y = 1 3 39. through the point A 23, 3B, opens up 40. through the point A -2, -222B, opens left 41. through the point 13, 22, symmetric with respect to the x-axis 42. through the point 12, -42, symmetric with respect to the y-axis Write an equation for each parabola. See Example 5. 43. vertex 14, 32, focus 14, 52 44. vertex 1-2, 12, focus 1-2, -32 45. vertex 1-5, 62, directrix x = -12 46. vertex 11, 22, directrix x = 4 Determine the two equations necessary to graph each horizontal parabola using a graphing calculator, and graph it in the viewing window indicated. See Example 2. 47. x = 3y2 + 6y - 4; 3-10, 24 by 3-4, 44 48. x = -2y2 + 4y + 3; 3-10, 6.54 by 3-4, 44 49. x + 2 = -1y + 122; 3-10, 24 by 3-4, 44 50. x - 5 = 21y - 222; 3-2, 124 by 3-2, 64 Solve each problem. See Example 6. 51. (Modeling) Radio Telescope Design The U.S. Naval Research Laboratory designed a giant radio telescope that had diameter 300 ft and maximum depth 44 ft. (Data from Mar, J., and H. Liebowitz, Structure Technology for Large Radio and Radar Telescope Systems, The MIT Press.) (a) Write an equation of a parabola that models the cross section of the dish if the vertex is placed at the origin and the parabola opens up. (b) The receiver must be placed at the focus of the parabola. How far from the vertex, to the nearest tenth of a foot, should the receiver be located?
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