A)
Axis of symmetry is y = – 7.
B)
Axis of symmetry is x =7.
C)
Axis of symmetry is y =7.
D)
Axis of symmetry is x = – 7.
34)
x =(y – 8)2– 7
21
A)
Axis of symmetry is y =8.
B)
Axis of symmetry is x =8.
C)
Axis of symmetry is y = – 8.
D)
Axis of symmetry is x = – 8.
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
35)
16x2=144 +y2
A)
ellipse
B)
parabola
C)
circle
D)
hyperbola
22
Give the coordinates for the vertex for the parabola.
36)
x = – 2(y + 4)2– 8
A)
(–8, –4)
B)
(–4, –8)
C)
(–8, 4)
D)
(4, –8)
Write the standard form of the equation of the circle with the given center and radius.
37)
Center (0, –9), r =10
A)
x2+ (y – 9)2=10
B)
(x + 9)2+ y2=100
C)
(x – 9)2+ y2=100
D)
x2+ (y + 9)2=100
Find the vertices of the hyperbola with the given equation.
38)
y2
25 –x2
16 = 1
A)
(0, –5), (0, 5)
B)
(0, –4), (0, 4)
C)
(–5, 0), (5, 0)
D)
(–4, 0), (4, 0)
Solve the system by the substitution method.
39)
x + y =8
y =x2– 12x + 36
A)
{(4, 12), (7, 1)}
B)
{(–4, 12), (–7, 15)}
C)
{(4, 4), (7, 1)}
D)
{(6, 2)}
40)
xy =27
x2+y2=90
A)
{(9, 3), (–9, –3), (9, –3), (–9, 3)}
B)
{(–9, –3), (–3, –9), (–9, 3), (–3, 9)}
C)
{(9, 3), (–9, –3), (3, 9), (–3, –9)}
D)
{(9, 3), (3, 9), (9, –3), (3, –9)}
Sketch the ellipse for the equation.
41)
(x – 1)2
16 +y2
36 = 1
A)
B)
C)
D)
24
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph
the equation.
42)
x2+y2+ 6x – 10y + 18 = 0
A)
(x – 3)2+(y + 5)2=16
center (3, –5), r =4
B)
(x + 3)2+(y – 5)2=16
center (–3, 5), r =4
C)
(x – 3)2+(y – 5)2=16
center (3, 5), r =4
D)
(x + 3)2+(y + 5)2=16
center (–3, –5), r =4
Sketch the ellipse for the equation.
43)
(x + 1)2
16 +(y + 2)2
9= 1
A)
B)
C)
D)
Solve the problem.
44)
The area of a rectangular piece of cardboard shown is 555 square inches. The cardboard is used to
make an open box by cutting a 2–inch square from each corner and turning up the sides. If the
box is to have a volume of 726 cubic inches, find the dimensions of the cardboard that must be
used.
A)
15 in. by 37 in.
B)
11 in. by 31 in.
C)
17 in. by 39 in.
D)
13 in. by 35 in.
Graph the ellipse.
45)
4x2+y2=24
A)
B)
27
C)
D)
Determine whether the system is a nonlinear system or a linear system.
46)
y =x2+8
x2+y2= 16
A)
linear system
B)
nonlinear system
Write the standard form of the equation of the circle with the given center and radius.
47)
Center (0, 9), r =3
A)
(x – 9)2+ y2=9
B)
(x + 9)2+ y2=9
C)
x2+ (y + 9)2=3
D)
x2+ (y – 9)2=3
Solve the system by the addition method.
48)
x2– 3y2= 1
4x2+ 3y2=79
A)
{(4, 5), (–4, –5)}
B)
{(5, 4), (–5, 4), (5, –4), (–5, –4)}
C)
{(5, 4), (–5, –4)}
D)
{(4, 5), (–4, 5), (4, –5), (–4, –5)}
Solve the problem.
49)
The area of a garden is 480 square feet, and the length of its diagonal is 34 feet. Find the
dimensions of the garden.
A)
32 ft by 15 ft
B)
8 ft by 60 ft
C)
120 ft by 4 ft
D)
16 ft by 30 ft
Solve the system.
50)
x2+y2=1
x + y =1
A)
{(–1, 0), (0, 1)}
B)
{(1, 0), (0, –1)}
C)
{(–1, 0), (0, –1)}
D)
{(1, 0), (0, 1)}
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
51)
16y2=400 +16x2
A)
parabola
B)
circle
C)
ellipse
D)
hyperbola
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
29
52)
x =5+(y +6)2
A)
parabola
B)
hyperbola
C)
circle
D)
ellipse
30
Solve the problem.
53)
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
A)
4
9 feet from the base
B)
21
4 feet from the base
C)
9
16 feet from the base
D)
17
9 feet from the base
Sketch the ellipse for the equation.
31
54)
x2
25 +(y + 2)2
49 = 1
A)
B)
C)
D)
Use vertices and asymptotes to graph the hyperbola.
32
55)
36y2–9x2=324
A)
B)
C)
D)
Solve the system by the substitution method.
56)
3y – x =10
x2+y2–100 = 0
A)
{(–10, 0), (8, 6)}
B)
0, 10
3, 6, 16
3
C)
{(10, 0), (–10, 0), (8, 6)}
D)
0, 10
3, 0, –10
3, 6, 16
3
Give the coordinates for the vertex for the parabola.
57)
x =y2+ 8y + 19
A)
(–4, 3)
B)
(0, 4)
C)
(3, –4)
D)
(19, 0)
A)
D)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
58)
x2=16 +(y +4)2
34
A)
D)
A)
ellipse
B)
circle
C)
hyperbola
D)
parabola
Solve the system by the addition method.
59)
7x2+y2=49
7x2–y2=49
A)
{(7, 0), (–7, 0)}
B)
{(0, 7), (0, –7)}
C)
{(0, 7), (0, –7)}
D)
{( 7, 0), (–7, 0)}
Solve the problem.
60)
A system for tracking ships indicated that a ship lies on a hyperbolic path described by
6x2–y2=69. The process is repeated and the ship is found to lie on a hyperbolic path described
by y2–2x2=31. If it is known that the ship is located in the first quadrant of the coordinate
system, determine its exact location.
A)
(–5, –9)
B)
(9, 5)
C)
(5, 9)
D)
(–9, –5)
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph
the equation.
61)
x2+y2– 4y – 0 = 0
A)
x2+(y + 2)2=4
center (0, –2), r =2
B)
(x – 2)2+y2=4
center (2, 0), r =2
36
C)
(x + 2)2+y2=4
center (–2, 0), r =2
D)
x2+(y – 2)2=4
center (0, 2), r =2
Solve the system by the substitution method.
62)
xy = 1
–7x – y = – 8
A)
1, 1
B)
{(–7, 7), (–1, 1)}
C)
1
7, 7, 1, 1
D)
7, 1
7, 1, 1
63)
x – 2y = 3
x2– xy = 20
A)
(–5, –1), 8, 11
2
B)
(–5, –1), 11
2, 8
C)
(5, 1), –11
2, –8
D)
(5, 1), –8, –11
2
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
A)
y =9
7x2
B)
y =3
7x2
C)
y =7
9x2
D)
y =7
3x2
65)
A rectangular coordinate system with coordinates in miles is placed with the origin at the center
of Los Angeles. A university is located 27.8 miles east and 30.8 miles north of central Los Angeles.
A seismograph on the campus shows a small earthquake occurred. The quake’s epicenter is 25.6
miles from the university. Write the standard form of the equation for the set of points that could
be the epicenter of the quake.
A)
(x +27.8)2+(y +30.8)2=25.6
B)
(x –27.8)2+(y –30.8)2=25.6
C)
(x –27.8)2+(y –30.8)2=655.36
D)
(x +27.8)2+(y +30.8)2=655.36
Graph the ellipse.
38
66)
9x2+6y2=54
A)
B)
C)
D)
39
Give the center and radius of the circle.
67)
x2+ y2+ 4x +
8y + 16 = 0
A)
center: (2, 4); r =4
B)
center: (4, 2); r =4
C)
center: (–4, –2); r =2
D)
center: (–2, –4); r =2
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
68)
x = – (y + 4)2+ 2
A)
(–4, 2)
B)
(4, 2)
C)
(2, –4)
D)
(2, 4)
Solve the problem.
69)
Find the dimensions of a rectangle whose perimeter is 50 feet and whose area is 150 square feet.
A)
10 ft by 15 ft
B)
11 ft by 14 ft
C)
9 ft by 14 ft
D)
9 ft by 16 ft
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
70)
x + 74 – 40y = – 5y2
A)
hyperbola
B)
ellipse
C)
circle
D)
parabola
40