Solve the problem.
106)
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. At some point along the road from the
lowest point of the cable, the cable is 1.44 inches above the roadway. Find the distance between that
point and the base of the nearest tower.
106)
A)
12.2 in.
B)
28.2 in.
C)
11.8 in.
D)
28 in.
Find the vertex, focus, and directrix of the parabola with the given equation.
107)
(y + 3)2=8x
107)
A)
vertex: (0, –3)
focus: (–4, –3)
directrix: x = – 2
B)
vertex: (0, 3)
focus: (4, 3)
directrix: x =0
C)
vertex: (0, –3)
focus: (2, –3)
directrix: x = – 2
D)
vertex: (–3, 0)
focus: (2, –3)
directrix: x = – 5
Graph the semi–ellipse.
108)
y = – 16 –9x2
108)
57
A)
B)
C)
D)
Is the relation a function?
109)
x = – (y + 6)2+ 1
109)
A)
Yes
B)
No
Graph the parabola.
58
110)
y2=5x
110)
A)
B)
C)
D)
Find the standard form of the equation of the parabola using the information given.
111)
Vertex: (3, –6); Focus: (5, –6)
111)
A)
(y +6)2=8(x –3)
B)
(y +6)2= – 8(x –3)
C)
(x +3)2= – 4(y –6)
D)
(x +3)2=4(y –6)
Use the relation’s graph to determine its domain and range.
112)
x2
9+y2
4= 1
112)
A)
Domain: [–2, 2]
Range: [–3, 3]
B)
Domain: [–3, 3]
Range: [–2, 2]
C)
Domain: [–3, 3]
Range: (–, )
D)
Domain: (–3, 3)
Range: (–2, 2)
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.
113)
x2+y2=145
x + y = – 17
113)
A)
{(–8, –9), (–9, –8)}
B)
{(8, 9), (9, 8)}
C)
{(8, –9), (9, –8)}
D)
{(–8, 9), (–9, 8)}
Use the center, vertices, and asymptotes to graph the hyperbola.
60
114)
(y – 1)2–(x + 2)2=2
114)
A)
B)
C)
D)
61
Find the vertices and locate the foci for the hyperbola whose equation is given.
115)
64x2–100y2=6400
115)
A)
vertices: (–10, 0), (10, 0)
foci: (–241, 0), (241, 0)
B)
vertices: (–10, 0), (10, 0)
foci: (–6, 0), (6, 0)
C)
vertices: (0, –10), (0, 10)
foci: (0, –241), (0, 241)
D)
vertices: (–8, 0), (8, 0)
foci: (–241, 0), (241, 0)
Determine the direction in which the parabola opens, and the vertex.
116)
y =x2+ 4x – 1
116)
A)
Opens to the right; (–5, 2)
B)
Opens upward; (–2, –5)
C)
Opens upward; (2, –5)
D)
Opens to the right; (–5, –2)
Graph the ellipse and locate the foci.
117)
x2
5
2
+y2
9
2
= 1
Round to the nearest tenth if necessary.
117)
62
A)
foci (0, 1.4) and (0, –1.4)
B)
foci (0, 1.4) and (0, –1.4)
C)
foci (1.5, 0) and (0, –1.5)
D)
foci (1.4, 0) and (0, –1.4)
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
118)
(x – 1)2
81 –(y – 2)2
100 = 1
118)
A)
Center: (–1, –2); Vertices: (–10, –2) and (8, –2); Foci: (–1–181, –2) and (–1+181, –2)
B)
Center: (1, 2); Vertices: (–8, –2) and (10, –2); Foci: (1–181, –2) and (1+181, –2)
C)
Center: (1, 2); Vertices: (–8, 2) and (10, 2); Foci: (1 –181, 2) and (1+181, 2)
D)
Center: (1, 2); Vertices: (–7, 2) and (11, 2); Foci: (2+181, 3) and (3+181, 3)
Graph the parabola.
63
119)
x2= – 20y
119)
A)
B)
C)
D)
Graph the ellipse.
64
120)
(x + 1)2
9+(y – 1)2
16 = 1
120)
A)
B)
C)
D)
Find the vertices and locate the foci for the hyperbola whose equation is given.
121)
y2
36 –x2
4= 1
121)
A)
vertices: (–6, 0), (6, 0)
foci: (–2, 0), (2, 0)
B)
vertices: (0, –6), (0, 6)
foci: (0, –210), (0, 210)
C)
vertices: (–2, 0), (2, 0)
foci: (–210, 0), (210, 0)
D)
vertices: (0, –6), (0, 6)
foci: (–210, 0), (210, 0)
Convert the equation to the standard form for a hyperbola by completing the square on x and y.
122)
x2–y2+ 6x + 2y + 7 = 0
122)
A)
(y + 3)2
4–(x – 1)2
36 = 1
B)
(y + 3)2–(x – 1)2= 1
C)
(x + 3)2–(y – 1)2= 1
D)
(x + 3)2+(y – 1)2= 1
Find the standard form of the equation of the parabola using the information given.
123)
Vertex: (9, –8); Focus: (9, –2)
123)
A)
(y –8)2=28(x +9)
B)
(y –8)2= – 28(x +9)
C)
(x –9)2=24(y +8)
D)
(x –9)2= – 24(y +8)
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.
124)
x2
16 +y2
9= 1
y =3
124)
A)
{(3, 0)}
B)
{(0, 3)}
C)
{(0, 3), (0, –3)}
D)
{(3, 3)}
Graph the ellipse.
125)
16(x + 2)2+4(y – 2)2=64
125)
A)
B)
67
C)
D)
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
126)
(y – 2)2–64(x – 3)2=64
126)
A)
Center: (3, 2); Vertices: (3, –6) and (3, 10); Foci: (3, 2–65) and (3, 2+65)
B)
Center: (–3, –2); Vertices: (–3, –10) and (–3, 6); Foci: (–3, –2–65) and (–3, –2+65)
C)
Center: (3, 2); Vertices: (4, –5) and (4, 11); Foci: (4, 3–65) and (4, 3+65)
D)
Center: (3, 2); Vertices: (–3, –8) and (3, 8); Foci: (3, –65) and (3, 65)
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
127)
y = ± x2–4
127)
68
A)
Asymptotes: y = ± 3
4x
B)
Asymptotes: y = ± x
C)
Asymptotes: y = ± 4
3x
D)
Asymptotes: y = ± x
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7