C Challenge

Graph each pair of equations. Identify the conic section represented by the graph. Then write a single equation for the conic section.

63. y = 3 + 16 − ( x − 4 ) 2 y = 3 − 16 − ( x − 4 ) 2 table with 2 rows and 2 columns , row1 column 1 , y , column 2 equals 3 plus . square root of 16 minus . open , x minus 4 , close squared end root , row2 column 1 , y , column 2 equals 3 minus . square root of 16 minus . open , x minus 4 , close squared end root , end table
64. y = − 2 + x − 3 y = − 2 − x − 3 table with 2 rows and 2 columns , row1 column 1 , y , column 2 equals negative 2 plus , square root of x minus 3 end root , row2 column 1 , y , column 2 equals negative 2 minus , square root of x minus 3 end root , end table
65. Astronomy The table gives the diameters of three planets.
    1. Use a center of (0, 0) to graph a circle that represents the size of each planet.
    2. Write an equation representing the circular cross section through the center of each planet.

    Planet	Diameter (miles)
    Mercury	3031
    Mars	4222
    Earth	7926

66. 1. A circle contains the points (0, 0), (6, 8), and (7, 7). Find its equation by solving a system of three equations.
    2. Several parabolas contain the three points of part (a), but only one is described by a quadratic function. What is that function?

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

67. What is the radius of the circle with equation ( x + 5 ) 2 + ( y − 3 ) 2 = 144 ? open x plus 5 close squared . plus . open y minus 3 close squared . equals 144 question mark
68. Find the positive zero of the function y = x 2 + 2 x − 5 y equals , x squared , plus 2 x minus 5  by graphing. Enter your answer as a decimal to the nearest hundredth.
69. What is the distance between T ( 9 , − 5 ) t open 9 comma negative 5 close  and the center of the circle with equation ( x − 6 ) 2 + ( y + 1 ) 2 = 10 ? open x minus 6 close squared . plus . open y plus 1 close squared . equals 10 question mark
70. What is the common ratio in a geometric series if a 2 = 1 3 eh sub 2 , equals , 1 third  and a 5 = 8 81 ? eh sub 5 , equals , 8 eighty firsts , question mark  Enter your answer as a fraction.
71. Evaluate the sum ∑ n = 1 3 ( 1 n + 1 ) 2 . sum , from , n equals 1 , to , 3 , of . open . fraction 1 , over n plus 1 end fraction . close squared . .  Enter your answer as a decimal to the nearest hundredth.

Mixed Review

See Lesson 10-2.

72. What is an equation of a parabola opening left with vertex (0, 0) and focus ( − 3 , 0 ) ? negative 3 comma 0 close question mark

See Lesson 8-3.

For each rational function, find any points of discontinuity.

73. y = 2 x + 1 y equals . fraction 2 , over x plus 1 end fraction
74. y = 1 x 2 − 5 x + 6 y equals . fraction 1 , over x squared , minus 5 x plus 6 end fraction
75. y = 2 x − 1 x 2 + 4 y equals . fraction 2 x minus 1 , over x squared , plus 4 end fraction

See Lesson 7-3.

Evaluate each logarithm.

76. log 2 16 log base 2 , 16
77. log 5 25 log base 5 , 25
78. log 3 1 27 log base 3 . 1 twenty seventh
79. log 10,000 log , 10,000
80. log 36 6 log base 36 , 6
81. log 100 100 log base 100 . 100

Get Ready! To prepare for Lesson 10-4, do Exercises 82–84.

See Lesson 5-3.

Solve each equation.

82. x 2 + 11 x = − 18 x squared , plus 11 x equals negative 18
83. m 5 − 256 m = 0 m to the fifth , minus 256 m equals 0
84. p 4 + 32 = 12 p 2 p to the fourth , plus 32 equals , 12 p squared

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