C Challenge

61. Astronomy The sun is at a focus of Earth's elliptical orbit.
    1. Find the distance from the sun to the other focus.
    2. Refer to Exercise 43 for the definition of eccentricity. What is the eccentricity of the orbit?
    3. Write an equation of Earth's orbit. Assume that the major axis is horizontal.
62. Writing The area of a circle is π r 2 . pi , r squared , .  The area of an ellipse is π a b . pi eh b .  Explain the connection.

Standardized Test Prep

SAT/ACT

63. Which equation is represented by the circle shown?
    1. ( x − 1 ) 2 + ( y + 2 ) 2 = 4 open x minus 1 close squared . plus . open y plus 2 close squared . equals 4
    2. ( x + 1 ) 2 + ( y − 2 ) 2 = 4 open x plus 1 close squared . plus . open y minus 2 close squared . equals 4
    3. ( x + 2 ) 2 + ( y − 1 ) 2 = 4 open x plus 2 close squared . plus . open y minus 1 close squared . equals 4
    4. ( x − 2 ) 2 + ( y + 1 ) 2 = 4 open x minus 2 close squared . plus . open y plus 1 close squared . equals 4
64. Solve x + 2 x = 2 . square root of x plus , square root of 2 x end root end root . equals 2 .  Check for extraneous solutions.
    6. 2 , − 8 2 comma negative 8
    7. 0, 2
    8. 2
    9. − 8 , 1 negative 8 comma 1

65. The graph of which equation contains all the points in the table below?

    x	− 4 negative 4	− 2 negative 2	0	2	4
    y	0	± 3 plus minus square root of 3	± 2 plus minus 2	± 3 plus minus square root of 3	0

    1. x 2 + 4 y 2 = 16 x squared , plus 4 , y squared , equals 16
    2. 4 x 2 + 16 y 2 = 144 4 x squared , plus 16 , y squared , equals 144
    3. 4 x 2 + 25 y 2 = 64 4 x squared , plus 25 , y squared , equals 64
    4. 9 x 2 + 4 y 2 = 81 9 x squared , plus 4 , y squared , equals 81

Short Response

66. Find the horizontal asymptote of y = 5 x + 7 x + 3 y equals . fraction 5 x plus 7 , over x plus 3 end fraction  by dividing the numerator by the denominator. Explain your steps.

Mixed Review

See Lesson 10-3.

Write an equation of a circle with the given center and radius.

67. center ( 1 , − 5 ) , open 1 comma negative 5 close comma  radius 3
68. center ( − 2 , 4 ) , open negative 2 comma 4 close comma  radius 9

See Lesson 8-4.

Simplify each expression. State any restrictions on the variable.

69. 3 x 6 x 2 − 9 x 5 fraction 3 x , over 6 , x squared , minus 9 , x to the fifth end fraction
70. x 2 − 36 x 2 + 5 x − 6 fraction x squared , minus 36 , over x squared , plus 5 x minus 6 end fraction
71. x 2 − 3 x − 10 x 3 + 8 fraction x squared , minus 3 x minus 10 , over x cubed , plus 8 end fraction

See Lesson 7-4.

Write each expression as a single logarithm.

72. log 3 + log 5 log 3 plus log 5
73. log 3 12 − log 3 2 log base 3 , 12 minus , log base 3 , 2
74. 3 log 2 − log 4 3 log 2 minus log 4

Get Ready! To prepare for Lesson 10-5, do Exercises 75–76.

See Lesson 2-3.

Write an equation of a line in slope-intercept form using the given information.

75. m = 2 m equals 2  and the y-intercept is 4
76. passes through (3, 1) and (9, 3)

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