Dut solutions to odd-numbered exercises. Finding the Vertex, Focus, and Directrix of a Parabola In Exercises 37-50, find the vertex, focus, and directrix of the parabola. Then sketch the parabola. 10.2 Introduct 63. Highway Desig parabolic curve to straight street to ar Write an equation of 37. y = r 38. y = -4x 39. y2 = -6x 41. x + 12y = 0 43. (x- 1)2 + 8(y + 2) = 0 44. (x + 5) + (y – 1)2 = 0 45. (y + 7)2 = 4(x - }) 47. y = (x – 2x + 5) 49. y + 6y + 8x + 25 = 0 50. x - 4x - 4y = 0 %3D 40. y = 3x e, called 42. x + y = 0 800 400- he parabola. %3D 46. (x + } = 4(y – 1) 48. x = (° + 2y + 33) rabola is a -400 -800 Finding the Vertex, Focus, and Directrix of a Parabola In Exercises 51-54, find the vertex, focus, 64. Road Design R and directrix of the parabola. Use a graphing utility to does not cros, graph the parabola. parabolic surfaces to road is 32 feet wide 51. x2 + 4x - 6y = – 10 52. x- 2r + 8y = -9 than it is on the sides 16. Focus: , 0) 18. Focus: (0, - 1) 23. Directrix: y = -4 53. y2 + x + y = 0 54. y - 4x - 4 = 0 Finding the Tangent Line at a Point on a Parabola In Exercises 55-60, find an equation of the tangent line to the parabola at the given point. 22. Directrix: x = 3 ough the point (4, 6) gh the point (- 3, -3) irough the point (-2, 5) xough the point (3, –2) 56. 55. x² = 3y X' Not drawn to scale 8. -4y (6.9) (a) Write an equation the origin that mo -8 4 8 Standard Equation of a Exercises 27-36, find the the equation of the parabola (b) How far from th surface 0.1 foot le 4- 8 12 -4 -4 9-6, -9) 65. Beam Deflection 58. * = 2y, (-3, ) 64 feet long and has aracteristics. 57. x = 2y, (4, 8) %3D The deflection of the 28. 59. y = - 2x, (-1, -2) 60. y = -2r, (2, -8) У shape of the deflected 61. Flashlight The light bulb in a flashlight is at the focus of the parabolic reflector, 1.5 centimeters from the vertex of the reflector (see figure). Write an equation for a cross section of the flashlight's reflector with its focus on the positive x-axis and its vertex at the origin. Focus (-3, 0) 4 8 12 Vertex (-4, 0) 8- Receiver (a) Write an equation the origin that mo 1.5 cm 3.5 ft - 8) (b) How far from the inch? =D4 4) 4.