A)
hyperbola
B)
ellipse
C)
parabola
D)
circle
Find the vertices of the hyperbola with the given equation.
36)
x2
81 –y2
1= 1
36)
A)
(–1, 0), (1, 0)
B)
(–9, 0), (9, 0)
C)
(0, –9), (0, 9)
D)
(0, –1), (0, 1)
Solve the problem.
37)
A local university is building a new arena to hold basketball games, indoor track meets, concerts,
etc. The arena will be elliptical in shape with external dimensions of 450 feet by 300 feet. Assume
that the center of the arena is the origin. Write an equation that models the shape of the new arena.
37)
A)
x2
2252+y2
1502= 1
B)
x2
4502+y2
3002= 1
C)
x2
1502+y2
2252= 1
D)
x2
3002+y2
4502= 1
Solve the system by the substitution method.
38)
x + y =3
(x – 2)2+(y + 5)2= 20
38)
A)
{(4, –1), (6, –3)}
B)
{(4, –1), (2, –7)}
C)
{(–1, 4), (–7, 2)}
D)
{(–1, 4), (–3, 6)}
Solve the problem.
39)
A rectangle has a diagonal of 17 feet and a perimeter of 46 feet. Find the rectangle’s dimensions.
39)
A)
8 ft by 15 ft
B)
15 ft by 16 ft
C)
8 ft by 30 ft or 15 ft by 16 ft
D)
8 ft by 30 ft
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
40)
4x2=36 –y2
40)
22
A)
ellipse
B)
circle
C)
parabola
D)
hyperbola
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.
41)
The sum of two numbers is –10 and their product is –144. Find the numbers.
41)
A)
–18 and 8 or 18 and –8
B)
–18 and –8 or 18 and 8
C)
–18 and 8
D)
18 and –8
C
Find the distance between the pair of points. Give an exact answer.
42)
(5, 1) and (–6, –3)
42)
A)
105 units
B)
137 units
C)
44 units
D)
137 units
B
A
Determine whether the system is a nonlinear system or a linear system.
43)
4x – y = 10
x2=9y + 11
43)
A)
nonlinear system
B)
linear system
Solve the system by the addition method.
44)
y2+2x2=28
y2–x2= 1
44)
A)
(3, 10), (3, –10)
B)
(4, 10), (4, –10), (–4, 10), (–4, –10)
C)
(3, 10), (3, –10), (–3, 10), (–3, –10)
D)
(4, 10), (4, –10)
C
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
45)
x = – y2+ 12y – 33
45)
A)
Axis of symmetry is x = – 6.
B)
Axis of symmetry is y =6.
24
A
C)
Axis of symmetry is y = – 6.
D)
Axis of symmetry is x =6.
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
46)
x =4(y – 9)2+ 8
46)
A)
(8, –9)
B)
(8, 9)
C)
(–8, –9)
D)
(–8, 9)
Sketch the ellipse for the equation.
47)
(x + 1)2
4+(y + 2)2
9= 1
47)
25
A)
B)
C)
D)
Solve the system by the addition method.
48)
x2–y2=29
x2+y2=35
48)
A)
{(4 2, 3), (–4 2, 3), (4 2, –3), (–4 2, –3)}
B)
{(4 2, 3), (–4 2, 3)}
C)
{(4 2, 3), (–4 2, –3)}
D)
{(0, 0)}
Find the vertices of the hyperbola with the given equation.
49)
y2
121 –x2
1= 1
49)
A)
(–1, 0), (1, 0)
B)
(0, –11), (0, 11)
C)
(–11, 0), (11, 0)
D)
(0, –1), (0, 1)
Solve the system by the substitution method.
50)
xy =9
x2+y2=82
50)
A)
{(1, 9), (9, 1), (1, –9), (9, –1)}
B)
{(–1, –9), (–9, –1), (–1, 9), (–9, 1)}
C)
{(1, 9), (–1, –9), (1, –9), (–1, 9)}
D)
{(1, 9), (–1, –9), (9, 1), (–9, –1)}
D
Find the vertices of the hyperbola with the given equation.
51)
4x2=144y2+576
51)
A)
(0, –12), (0, 12)
B)
(–12, 0), (12, 0)
C)
(0, –2), (0, 2)
D)
(–2, 0), (2, 0)
B
Write the standard form of the equation of the circle with the given center and radius.
52)
Center (0, –3), r =3
52)
A)
x2+ (y + 3)2=3
B)
x2+ (y – 3)2=3
C)
(x – 3)2+ y2=9
D)
(x + 3)2+ y2=9
A
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
53)
x2=144 +9y2
53)
A)
hyperbola
B)
ellipse
C)
circle
D)
parabola
A
27
B
Write the standard form of the equation of the circle with the given center and radius.
54)
Center (0, –6), r =1
54)
A)
(x – 6)2+ y2=1
B)
x2+ (y – 6)2=1
C)
x2+ (y + 6)2=1
D)
(x + 6)2+ y2=1
Solve the system by the addition method.
55)
x2– 3y2= 1
4x2+ 3y2=124
55)
A)
{(8, 5), (–8, 5), (8, –5), (–8, –5)}
B)
{(5, 8), (–5, –8)}
C)
{(5, 8), (–5, 8), (5, –8), (–5, –8)}
D)
{(8, 5), (–8, –5)}
Find the vertices of the hyperbola with the given equation.
56)
9y2–36x2=324
56)
A)
(0, –3), (0, 3)
B)
(0, –6), (0, 6)
C)
(–6, 0), (6, 0)
D)
(–3, 0), (3, 0)
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
57)
x = 2(y – 5)2– 2
57)
A)
horizontal; opens to right; (–2, –5)
B)
vertical; opens upward; (5, –2)
C)
vertical; opens upward; (–5, –2)
D)
horizontal; opens to right; (–2, 5)
Graph the ellipse.
28
58)
25x2+9y2=225
58)
A)
B)
C)
D)
29
Solve the system by the addition method.
59)
x2+y2=29
x2–y2= – 21
59)
A)
{(2, 5), (5, 2), (–2, –5), (–5, –2)}
B)
{(–2, –5), (–5, –2)}
C)
{(2, –5), (2, 5)}
D)
{(2, 5), (–2, 5), (2, –5), (–2, –5)}
Solve the problem.
60)
The area of a rectangular piece of cardboard shown is 720 square inches. The cardboard is used to
make an open box by cutting a 3–inch square from each corner and turning up the sides. If the box
is to have a volume of 1296 cubic inches, find the dimensions of the cardboard that must be used.
60)
A)
21 in. by 27 in.
B)
18 in. by 21 in.
C)
27 in. by 33 in.
D)
24 in. by 30 in.
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
61)
3x2+y2=48
61)
30
A)
ellipse
B)
parabola
C)
circle
D)
hyperbola
Provide an appropriate response.
62)
Write the standard form of the equation of the circle with center (–6, 3) and radius 10.
62)
A)
(x + 6)2+ (y – 3)2=100
B)
(x – 3)2+ (y + 6)2=10
C)
(x + 3)2+ (y – 6)2=10
D)
(x – 6)2+ (y + 3)2=100
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
63)
25x2=400 –y2
63)
A)
circle
B)
parabola
C)
hyperbola
D)
ellipse
Solve the problem.
64)
A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the
surface of the dish and are reflected to the focus, where the receiver is located. The satellite dish
shown has a diameter of 6 feet and a depth of 7 feet. The parabola is positioned in a rectangular
coordinate system with its vertex at the origin. Write an equation in the form of y = ax2 for the
parabola used to shape the dish.
(3, 7)
7 feet
64)
A)
y =7
3x2
B)
y =3
7x2
C)
y =9
7x2
D)
y =7
9x2
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
65)
x =(y – 5)2+ 3
65)
32
A)
Axis of symmetry is y =5.
B)
Axis of symmetry is x = – 5.
C)
Axis of symmetry is y = – 5.
D)
Axis of symmetry is x =5.
Use vertices and asymptotes to graph the hyperbola.
66)
x2
9–y2
36 = 1
66)
33
A)
B)
C)
D)
Solve the system by the substitution method.
67)
12x2+10y2=90
y = x +3
67)
A)
(0, –3), –30
11 , 3
11
B)
(0, –3), 30
11 , 63
11
C)
(0, 3), –30
11 , 3
11
D)
(0, 3), 30
11 , 63
11
Write the standard form of the equation of the circle with the given center and radius.
68)
Center (0, 0), r =3
68)
A)
x2+y2=3
B)
x2+y2=6
C)
x2–y2=3
D)
x2+y2=9
Find the midpoint of the line segment with the given end points.
69)
(9, –4) and (0, 7)
69)
A)
(9, 3)
B)
(9, –11)
C)
9
2, –11
2
D)
9
2, 3
2
D
D
Solve the problem.
70)
A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the
surface of the dish and are reflected to the focus, where the receiver is located. The satellite dish
shown has a diameter of 6 feet and a depth of 4 feet. The parabola is positioned in a rectangular
coordinate system with its vertex at the origin. The receiver should be placed at the focus (0, p). The
value of p is given by the equation a =1
4p . How far from the base of the dish should the receiver be
placed? [Hint: First write an equation in the form of y = ax2 for the parabola used to shape the
dish.]
(3, 4)
4 feet
70)
A)
17
9 feet from the base
B)
4
9 feet from the base
C)
21
4 feet from the base
D)
9
16 feet from the base
Find the vertices of the hyperbola with the given equation.
71)
x2
1–y2
100 = 1
71)
A)
(–10, 0), (10, 0)
B)
(–1, 0), (1, 0)
C)
(0, –1), (0, 1)
D)
(0, –10), (0, 10)
Find the midpoint of the line segment with the given end points.
72)
7
3, 5
4 and 2, –7
4
72)
A)
13
3, –1
2
B)
1
6, 3
2
C)
–1
6, –3
2
D)
13
6, –1
4
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
73)
y =x2+ 10x + 26
73)
A)
horizontal; opens to the right; (1, 5)
B)
horizontal; opens to the right; (1, –5)
C)
vertical; opens upward; (–5, 1)
D)
vertical; opens upward; (5, 1)
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
74)
x = – (y – 7)2– 1
74)
A)
Axis of symmetry is y =7.
B)
Axis of symmetry is y = – 7.
37
C)
Axis of symmetry is x = – 7.
D)
Axis of symmetry is x =7.
Solve the problem.
75)
The ferris wheel in the figure has a radius of 31 meters. The distance between the top of the ferris
wheel and the ground is 67 meters. The rectangular coordinate system shown has its origin on the
ground directly below the center of the wheel. Use the coordinate system to write the equation of
the circular wheel.
62 m
67 m
75)
A)
x2+(y –36)2=312
B)
x2+y2=312
C)
x2+(y –36)2=622
D)
x2+(y +36)2=312
The equation of a horizontal parabola is given. Determine how the parabola opens and find the parabola’s vertex.
76)
x = – (y + 1)2– 3
76)
A)
opens to right; (–1, –3)
B)
opens to left; (–3, –1)
C)
opens to left; (–3, 1)
D)
opens to left; (–1, –3)
Find the distance between the pair of points. Give an exact answer.
77)
(2, –5) and (4, –1)
77)
A)
2 5 units
B)
12 units
C)
2 units
D)
12 3 units
A
Solve the system by the addition method.
78)
8x2+y2=64
8x2–y2=64
78)
A)
{(2 2, 0), (–2 2, 0)}
B)
{(0, 2 2), (0, –2 2)}
C)
{(0, 8), (0, –8)}
D)
{(8, 0), (–8, 0)}
A
Find the midpoint of the line segment with the given end points.
79)
(3, 9) and (7, 5)
79)
A)
5, 7
B)
(–4, 4)
C)
– 2, 2
D)
(10, 14)
A
B
Find the standard form of the equation of the hyperbola.
80)
80)
A)
y2
16 –x2
4= 1
B)
x2
16 –y2
4= 1
C)
x2
4–y2
16 = 1
D)
y2
4–x2
16 = 1
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
81)
y = – (x + 6)2– 8
81)
A)
vertical; opens downward; (– 6, –8)
B)
horizontal; opens to left; (–8, 6)
C)
vertical; opens downward; (6, –8)
D)
horizontal; opens to left; (–8, – 6)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
82)
x2
25 –y2
16 = 1
82)