Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the equation to the graph.
1)
y2=9x
1)
A)
B)
C)
D)
1
2)
y2= – 9x
2)
A)
B)
C)
D)
2
3)
(x – 2)2=7(y – 2)
3)
A)
B)
C)
D)
3
4)
x2
4–y2
16 = 1
4)
A)
B)
C)
D)
4
5)
(y + 2)2=5(x + 2)
5)
A)
B)
C)
D)
5
6)
x2=9y
6)
A)
B)
C)
D)
6
7)
x2= – 10y
7)
A)
B)
C)
D)
7
8)
y2
4–x2
9= 1
8)
A)
B)
C)
D)
Is the relation a function?
9)
y2– 10y – x + 24 = 0
9)
A)
Yes
B)
No
8
Find the standard form of the equation of the hyperbola satisfying the given conditions.
10)
Foci: (0, –9), (0, 9); vertices: (0, –7), (0, 7)
10)
A)
y2
49 –x2
32 = 1
B)
x2
49 –y2
32 = 1
C)
y2
49 –x2
81 = 1
D)
x2
49 –y2
81 = 1
11)
Center: (6, 2); Focus: (3, 2); Vertex: (5, 2)
11)
A)
(x –2)2–(y –6)2
8= 1
B)
(x –2)2
8–(y –6)2= 1
C)
(x –6)2
8–(y –2)2= 1
D)
(x –6)2–(y –2)2
8= 1
Use the center, vertices, and asymptotes to graph the hyperbola.
12)
(y – 2)2–4(x – 3)2=4
12)
A)
B)
9
C)
D)
Find the solution set for the system by graphing both of the system’s equations in the same rectangular coordinate system
and finding points of intersection.
13)
x2+y2=145
x + y = – 17
13)
A)
{(–8, –9), (–9, –8)}
B)
{(–8, 9), (–9, 8)}
C)
{(8, 9), (9, 8)}
D)
{(8, –9), (9, –8)}
10
Find the standard form of the equation of the ellipse and give the location of its foci.
14)
14)
A)
x2
4+y2
16 = 1
foci at (0, 4) and (2, 0)
B)
x2
16 +y2
4= 1
foci at (0, –2 3) and (0, 2 3)
C)
x2
4+y2
16 = 1
foci at (0, –4) and (0, 4)
D)
x2
4+y2
16 = 1
foci at (0, –2 3) and (0, 2 3)
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
15)
y = ± x2–4
15)
11
A)
Asymptotes: y = ± 4
3x
B)
Asymptotes: y = ± 3
4x
C)
Asymptotes: y = ± x
D)
Asymptotes: y = ± x
Solve the problem.
16)
An experimental model for a suspension bridge is built. In one section, cable runs from the top of
one tower down to the roadway, just touching it there, and up again to the top of a second tower.
The towers are both 16 inches tall and stand 80 inches apart. Find the vertical distance from the
roadway to the cable at a point on the road 16 inches from the lowest point of the cable.
16)
A)
10.24 in.
B)
2.76 in.
C)
2.36 in.
D)
2.56 in.
Use the center, vertices, and asymptotes to graph the hyperbola.
12
17)
(y – 1)2–(x + 2)2=2
17)
A)
B)
C)
D)
13
Solve the problem.
18)
The arch beneath a bridge is semi–elliptical, a one–way roadway passes under the arch. The width
of the roadway is 30 feet and the height of the arch over the center of the roadway is 13 feet. Two
trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of 13 feet and
Truck 2 has an overall height of 12 feet. Draw a rough sketch of the situation and determine which
of the trucks can pass under the bridge.
18)
A)
Truck 2 can pass under the bridge, but Truck 1 cannot.
B)
Neither Truck 1 nor Truck 2 can pass under the bridge.
C)
Truck 1 can pass under the bridge, but Truck 2 cannot.
D)
Both Truck 1 and Truck 2 can pass under the bridge.
Graph the ellipse and locate the foci.
19)
4x2=64 –16y2
19)
A)
foci at ( 21, 0) and (–21, 0)
B)
foci at (0, 2 3) and (0, –2 3)
14
C)
foci at (2 5, 0) and (–2 5, 0)
D)
foci at (2 3, 0) and (–2 3, 0)
Find the standard form of the equation of the hyperbola.
20)
20)
A)
(x – 1)2
4–(y + 1)2
25 = 1
B)
(x – 1)2
25 –(y + 1)2
4= 1
C)
(y + 1)2
4–(x – 1)2
25 = 1
D)
(y + 1)2
25 –(x – 1)2
4= 1
15
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
21)
(x – 4)2–100(y – 1)2=100
21)
A)
Center: (4, 1); Vertices: (–6, 1) and (14, 1); Foci: (4 –101, 1) and (4+101, 1)
B)
Center: (4, 1); Vertices: (10, 1) and (–10, 1); Foci: (–101, 1) and ( 101, 1)
C)
Center: (–4, –1); Vertices: (–14, –1) and (6, –1); Foci: (–4–101, 1) and (–4+101, 1)
D)
Center: (4, 1); Vertices: (–5, 2) and (15, 2); Foci: (5–101, 2) and (5+101, 2)
Graph the ellipse and locate the foci.
22)
x2
49 +y2
25 = 1
22)
A)
foci at (0, 39) and (0, –39)
B)
foci at (2 6, 0) and (–2 6, 0)
16
C)
foci at (0, 2 6) and (0, –2 6)
D)
foci at ( 39, 0) and (–39, 0)
Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
23)
x2+ 2x + 6y – 11 = 0
23)
A)
(x + 1)2= – 6(y – 2)
B)
(x – 1)2= – 6(y – 2)
C)
(x + 1)2= – 6(y + 2)
D)
(x – 1)2=6(y – 2)
Convert the equation to the standard form for an ellipse by completing the square on x and y.
24)
36x2+4y2– 72x + 16y – 92 = 0
24)
A)
(x – 1)2
36 +(y + 2)2
4= 1
B)
(x + 2)2
4+(y – 1)2
36 = 1
C)
(x – 1)2
4+(y + 2)2
36 = 1
D)
(x + 1)2
4+(y – 2)2
36 = 1
17
Find the foci of the ellipse whose equation is given.
25)
(x – 3)2
25 +(y + 3)2
36 = 1
25)
A)
foci at (3, –3–11) and (3, –3+11)
B)
foci at (4, –3–11) and (4, –3+11)
C)
foci at (–3, 3–11) and (–3, 3+11)
D)
foci at (–3, –3–11) and (–3, –3+11)
Find the solution set for the system by graphing both of the system’s equations in the same rectangular coordinate system
and finding points of intersection.
26)
25x2+y2=25
y2–25x2=25
26)
A)
{(0, –5)}
B)
{(0, 25)}
C)
{(0, –5), (0, 5)}
D)
{(5, 0), (5, 0)}
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
27)
36y2–4x2=144
27)
18
A)
Asymptotes: y = ± 1
3x
B)
Asymptotes: y = ± 1
3x
C)
Asymptotes: y = ± 3x
D)
Asymptotes: y = ± 3x
19
Find the solution set for the system by graphing both of the system’s equations in the same rectangular coordinate system
and finding points of intersection.
28)
x2–y2=64
x2+y2=64
28)
A)
{(0, 8)}
B)
{(8, 0), (–8, 0)}
C)
{(0, 8), (0, –8)}
D)
{(8, 0)}
Use the relation’s graph to determine its domain and range.
29)
y2
9–x2
4= 1
29)
A)
Domain: (–, )
Range: (–, –3] or [3, )
B)
Domain: (–, –3] or [3, )
Range: (–, )
C)
Domain: (–, )
Range: (–, –3] and [3, )
D)
Domain: (–, –3] and [3, )
Range: (–, )
Graph the parabola.
20