B Apply

Find the foci for each equation of an ellipse.

36. 4 x 2 + 9 y 2 = 36 4 x squared , plus 9 , y squared , equals 36
37. 16 x 2 + 4 y 2 = 64 16 x squared , plus 4 , y squared , equals 64
38. 4 x 2 + 36 y 2 = 144 4 x squared , plus 36 , y squared , equals 144
39. 25 x 2 + 4 y 2 = 100 25 x squared , plus 4 , y squared , equals 100
40. 36 x 2 + 8 y 2 = 288 36 x squared , plus 8 , y squared , equals 288
41. 25 x 2 + 24 y 2 = 600 25 x squared , plus 24 , y squared , equals 600
42. Think About a Plan The open area south of the White House is known as the Ellipse, or President's Park South. It is 902 ft wide and 1058 ft long. Assume the origin is at the center of the President's Park South. What is the equation of the ellipse in standard form?
    • How does the length and width of the ellipse relate to the equation?
    • What does the center at the origin tell you?
    • How can you write the equation of the ellipse in standard form?
43. The eccentricity of an ellipse is a measure of how nearly circular it is. Eccentricity is defined as c a , c over eh , comma  where c is the distance from the center to a focus and a is the distance from the center to a vertex.
    1. Find the eccentricity of an ellipse with foci ( ± 9 , 0 ) open plus minus 9 comma 0 close  and vertices ( ± 10 , 0 ) . open plus minus 10 comma 0 close .
    2. Find the eccentricity of an ellipse with foci ( ± 1 , 0 ) open plus minus 1 comma 0 close  and vertices ( ± 10 , 0 ) . open plus minus 10 comma 0 close .
    3. Describe the shape of an ellipse that has an eccentricity close to 0.
    4. Describe the shape of an ellipse that has an eccentricity close to 1.

Write an equation for each ellipse.

44. 
45. 
46. 
47. Open-Ended Find a real-world design that uses ellipses. Place a coordinate grid over the design and write an equation of the ellipse.

Write an equation of an ellipse in standard form with center at the origin and with the given characteristics.

48. focus (1, 0), width 4
49. a = 5 , b = 2 , eh equals 5 comma b equals 2 comma  width 10
50. vertex ( − 11 , 0 ) , open negative 11 comma 0 close comma  co-vertex (0, 9)
51. height 29, width 53
52. focus ( − 2 , 0 ) , open negative 2 comma 0 close comma  co-vertex ( 0 , − 12 ) open 0 comma negative 12 close
53. c 2 = 68 , c squared , equals 68 comma  vertex ( 0 , − 18 ) open 0 comma negative 18 close
54. focus (0, 3 2 3 square root of 2 ), height 19
55. focus (2, 0), x-intercept 4
56. focus ( 0 , − 5 ) , open 0 comma negative 5 close comma  y-intercept 8
57. focus (3, 0), x-intercept − 6 negative 6
58. a = 3 , b = 2 , eh equals 3 comma b equals 2 comma  width 4
59. a = 2 5 , b = 3 2 , eh equals 2 square root of 5 comma b equals 3 square root of 2 comma  width 6 2 6 square root of 2
60. Aerodynamics Scientists used the Transonic Tunnel at NASA Langley Research Center, Virginia, to study the dynamics of air flow. The elliptical opening of the Transonic Tunnel is 82 ft wide and 58 ft high. What is an equation of the ellipse?

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