Chapter 13 the way the parabola opens, and the vertex

Write the standard form of the equation of the circle with the given center and radius.

71)

Center (–2, 0), r =10

A)

(x – 2)2+ y2=100

B)

x2+ (y + 2)2=10

C)

x2+ (y – 2)2=10

D)

(x + 2)2+ y2=100

The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and

the vertex.

72)

x = – (y – 9)2– 3

72)

A)

horizontal; opens to left; (–3, 9)

B)

vertical; opens downward; (–9, –3)

C)

horizontal; opens to left; (–3, –9)

D)

vertical; opens downward; (9, –3)

Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.

73)

x2=144 +9y2

73)

A)

circle

B)

ellipse

C)

hyperbola

D)

parabola

Find the vertices of the hyperbola with the given equation.

74)

x2

4–y2

25 = 1

74)

A)

(0, –5), (0, 5)

B)

(0, –2), (0, 2)

C)

(–2, 0), (2, 0)

D)

(–5, 0), (5, 0)

Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic

section.

41

75)

x2

16 –y2

36 = 1

75)

A)

parabola

B)

circle

C)

hyperbola

D)

ellipse

Give the center and radius of the circle described by the equation and graph the equation.

42

76)

x2+ y2=81

76)

A)

center (1, 1), r =9

B)

center (0, 0), r =9

C)

center (1, 1), r =3

D)

center (0, 0), r =3

43

Solve the system by the addition method.

77)

x2+y2– 4x + 6y – 12 = 0

x2–y2– 4x – 6y – 30 = 0

77)

A)

{(7, –3), (3, –3)}

B)

{(2, 2), (2, –8)}

C)

{(7, –3), (–3, –3)}

D)

{(2, –2), (2, 8)}

The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and

the vertex.

78)

x = – y2+ 6y – 3

78)

A)

vertical; opens downward; (–3, 6)

B)

horizontal; opens to the left; (6, –3)

C)

vertical; opens downward; (3, 6)

D)

horizontal; opens to the left; (6, 3)

Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic

section.

79)

16x2+9y2=144

79)

44

A)

ellipse

B)

parabola

C)

circle

D)

hyperbola

Find the vertices of the hyperbola with the given equation.

80)

16y2=64x2+1024

80)

A)

(0, –4), (0, 4)

B)

(–8, 0), (8, 0)

C)

(–4, 0), (4, 0)

D)

(0, –8), (0, 8)

45

Solve the system by the addition method.

81)

5x2– 5y2=60

2x2+ 5y2=52

81)

A)

{(4, 2), (2, 4), (–4, –2), (–2, –4)}

B)

{(–4, –2), (–2, –4)}

C)

{(4, 2), (–4, 2), (4, –2), (–4, –2)}

D)

{(4, –2), (4, 2)}

Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic

section.

82)

3x2+y2=27

82)

A)

hyperbola

B)

circle

46

C)

ellipse

D)

parabola

Solve the system by the substitution method.

83)

x2= y2+ 39

x – y = 3

83)

A)

{(8, –5)}

B)

{(–8, 5)}

C)

{(–8, –5)}

D)

{(8, 5)}

Graph the ellipse.

84)

10x2+25y2=250

84)

47

A)

B)

C)

D)

Give the center and radius of the circle.

85)

(x – 7)2+ (y – 9)2=100

85)

A)

center: (7, 9); r =10

B)

center: (– 7, – 9); r =100

C)

center: (7, 9); r =100

D)

center: (– 7, – 9); r =10

48

Solve the problem.

86)

The rectangular plot of land shown in the figure is to be fenced along three sides using 39 feet of

fencing. No fencing is to be placed along the river’s edge. The area of the plot is 154 square feet.

What are its dimensions?

A)

28 ft by 5.5 ft

B)

11 ft by 14 ft

C)

22 ft by 7 ft or 28 ft by 5.5 ft

D)

11 ft by 14 ft or 28 ft by 5.5 ft

Graph the ellipse.

87)

9x2+25y2=225

87)

A)

B)

49

C)

D)

50

Solve the problem.

88)

A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 6) and then

moves closer and closer to the line y =18

5x as it gets farther from the tracking station at the origin.

Find the equation that describes the path of the satellite if the center of the hyperbola is at (0, 0).

(0, 6)

y =18

5x

A)

x2

36 –y2

54

5

2= 1

B)

y2

36 –x2

25

9

= 1

C)

y2

25

9

–x2

36 = 1

D)

x2

54

5

2–y2

36 = 1

Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic

section.

89)

x2=27 –3(y +3)2

89)

51

A)

parabola

B)

hyperbola

C)

ellipse

D)

circle

Determine whether the system is a nonlinear system or a linear system.

90)

4x – y = 10

x =8y + 11

90)

A)

nonlinear system

B)

linear system

Use vertices and asymptotes to graph the hyperbola.

52

91)

x2–9y2=36

91)

A)

B)

C)

D)

Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph

the equation.

53

92)

x2+y2+ 8x – 0 = 0

92)

A)

x2+(y + 4)2=16

center (0, – 4), r =4

B)

x2+(y – 4)2=16

center (0, 4), r =4

C)

(x – 4)2+y2=16

center (4, 0), r =4

D)

(x + 4)2+y2=16

center (– 4, 0), r =4

54

Find the vertices of the hyperbola with the given equation.

93)

y2

1–x2

25 = 1

93)

A)

(–1, 0), (1, 0)

B)

(0, –5), (0, 5)

C)

(0, –1), (0, 1)

D)

(–5, 0), (5, 0)

Let x represent one number and let y represent the other number. Use the given conditions to write a system of

nonlinear equations. Solve the system and find the numbers.

94)

The sum of two squares of two numbers is 29, and the difference of their squares is 21. Find the

numbers.

A)

5 and 2, –5 and 2, or 5 and –2

B)

5 and 2

C)

5 and 2 or –5 and –2

D)

5 and 2, –5 and 2, 5 and –2, or –5 and –2

The equation of a horizontal parabola is given. Determine how the parabola opens and find the parabola’s vertex.

95)

x =(y + 5)2– 10

95)

A)

opens to right; (–10, –5)

B)

opens to right; (–10, 5)

C)

opens to left; (–5, –10)

D)

opens to right; (–5, –10)

Provide an appropriate response.

96)

Write the standard form of the equation of the circle with center (1, –4) and radius 2.

A)

(x – 1)2+ (y + 4)2=4

B)

(x + 4)2+ (y – 1)2=2

C)

(x – 4)2+ (y + 1)2=2

D)

(x + 1)2+ (y – 4)2=4

Find the standard form of the equation of the hyperbola.

97)

A)

x2

25 –y2

16 = 1

B)

y2

16 –x2

25 = 1

C)

x2

16 –y2

25 = 1

D)

y2

25 –x2

16 = 1

Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic

section.

98)

2x2=98 +2y2

98)

A)

parabola

B)

ellipse

56

C)

hyperbola

D)

circle

Solve the system by the substitution method.

99)

–13x – y =32

y =x2+ 10

99)

A)

{(–6, 26), (–7, 39)}

B)

{(6, 46), (–7, 59)}

C)

{(6, 46), (7, 59)}

D)

{(–6, 46), (–7, 59)}

Give the center and radius of the circle described by the equation and graph the equation.

100)

(x +1)2+(y –2)2=4

100)

57

A)

center (1, –2), r =2

B)

center (1, 2), r =2

C)

center (–1, 2), r =2

D)

center (–1, –2), r =2

Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph

the equation.

101)

x2+y2+ 12x + 2y + 28 = 0

101)

58

A)

(x – 6)2+(y – 1)2=9

center (6, 1), r =3

B)

(x + 6)2+(y + 1)2=9

center (–6, –1), r =3

C)

(x + 6)2+(y – 1)2=9

center (–6, 1), r =3

D)

(x – 6)2+(y + 1)2=9

center (6, –1), r =3

Solve the system by the substitution method.

102)

x – y =1

(x – 2)2+(y + 5)2= 20

102)

A)

{(–1, 0), (–7, 6)}

B)

{(0, –1), (–2, –3)}

C)

{(0, –1), (6, –7)}

D)

{(–1, 0), (–3, –2)}

Give the center and radius of the circle described by the equation and graph the equation.

59

103)

(x –3)2+(y –1)2=9

103)

A)

center (3, 1), r =3

B)

center (3, –1), r =3

C)

center (–3, 1), r =3

D)

center (–3, –1), r =3

Use vertices and asymptotes to graph the hyperbola.

60