A)
B)
C)
D)
Solve the problem.
105)
A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 156 feet and a
maximum height of 25 feet. Find the height of the arch at 15 feet from its center.
105)
A)
B)
C)
28.1 ft
D)
Graph the ellipse.
57
106)
(x + 1)2
16 +(y – 2)2
9= 1
106)
A)
B)
C)
D)
Find the focus and directrix of the parabola with the given equation.
107)
y2= – 16x
107)
A)
B)
C)
focus: (–4, 0)
directrix: x =4
D)
Find the standard form of the equation of the hyperbola satisfying the given conditions.
108)
Endpoints of transverse axis: (0, –8), (0, 8); asymptote: y =4
3x
108)
A)
B)
C)
y2
36 –x2
64 = 1
D)
Graph the parabola with the given equation.
109)
(y – 2)2= – 5(x + 1)
109)
A)
B)
59
C)
D)
Solve the problem.
110)
Two LORAN stations are positioned 252 miles apart along a straight shore. A ship records a time
difference of 0.00097 seconds between the LORAN signals. (The radio signals travel at 186,000
miles per second.) Where will the ship reach shore if it were to follow the hyperbola corresponding
to this time difference? If the ship is 100 miles offshore, what is the position of the ship?
110)
A)
90 miles from the master station, (100, 136.1)
B)
36 miles from the master station, (100, 136.1)
C)
36 miles from the master station, (136.1, 100)
D)
90 miles from the master station, (136.1, 100)
Graph the parabola with the given equation.
111)
(x + 2)2= – 5(y + 1)
111)
60
A)
B)
C)
D)
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
112)
4x2–9y2=36
112)
61
A)
Asymptotes: y = ± 3
2x
B)
Asymptotes: y = ± 2
3x
C)
Asymptotes: y = ± 3
2x
D)
Asymptotes: y = ± 2
3x
Find the focus and directrix of the parabola with the given equation.
113)
x2=4y
113)
A)
B)
C)
focus: (0, 1)
directrix: y = – 1
D)
Find the standard form of the equation of the ellipse and give the location of its foci.
114)
114)
A)
x2
4+y2
81 = 1
foci at (–77, 0) and ( 77, 0)
B)
x2
81 +y2
4= 1
foci at (–9, 0) and (9, 0)
C)
x2
81 +y2
4= 1
foci at (–77, 0) and ( 77, 0)
D)
x2
81 –y2
4= 1
foci at (–77, 0) and ( 77, 0)
Is the relation a function?
115)
y =x2+ 8x + 18
115)
A)
Yes
B)
No
A
Find the standard form of the equation of the parabola using the information given.
116)
Focus: (–3, 0); Directrix: y = – 4
116)
A)
(x + 3)2=8(y + 2)
B)
(y + 2)2=8(x + 3)
C)
(y + 3)2=8(x + 2)
D)
(x + 2)2=8(y + 3)
A
C
Use the relation’s graph to determine its domain and range.
117)
x2
4–y2
36 = 1
117)
A)
Domain: (–, )
Range: (–, –2) or (2, )
B)
Domain: (–, –2] or [2, )
Range: (–, )
C)
Domain: (–, –2] and [2, )
Range: (–, )
D)
Domain: (–, )
Range: (–, )
Find the standard form of the equation of the parabola using the information given.
118)
Focus: (0, –23); Directrix: y =23
118)
A)
B)
C)
y2= – 23x
D)
Find the foci of the ellipse whose equation is given.
119)
36(x – 3)2+25(y + 1)2=900
119)
A)
foci at (3, –1–11) and (3, –1+11)
B)
foci at (–1, 3–11) and (–1, 3+11)
C)
foci at (4, –1–11) and (4, –1+11)
D)
foci at (–3, –1–11) and (–3, –1+11)
64
Find the vertices and locate the foci for the hyperbola whose equation is given.
120)
y2
36 –x2
4= 1
120)
A)
vertices: (0, –6), (0, 6)
foci: (0, –210), (0, 210)
B)
vertices: (–6, 0), (6, 0)
foci: (–2, 0), (2, 0)
C)
vertices: (0, –6), (0, 6)
foci: (–210, 0), (210, 0)
D)
vertices: (–2, 0), (2, 0)
foci: (–210, 0), (210, 0)
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.
121)
x =(y +4)2– 1
(x –4)2+(y +4)2= 1
121)
A)
{(–1, –4)}
B)
{(4, –4)}
C)
{(–1, –4), (4, –4)}
D)
D
Convert the equation to the standard form for a hyperbola by completing the square on x and y.
122)
9x2–16y2+ 18x – 32y – 151 = 0
122)
A)
(x + 1)2
16 –(y + 1)2
9= 1
B)
(x + 1)2
9–(y + 1)2
16 = 1
C)
(x – 1)2
16 –(y + 1)2
9= 1
D)
(x + 1)2
16 –(y – 1)2
9= 1
A
65
A
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.
123)
x =y2–7
x =y2–7y
123)
A)
B)
C)
{(1, –6)}
D)
Use the center, vertices, and asymptotes to graph the hyperbola.
124)
(y + 2)2
9–(x – 1)2
16 = 1
124)
A)
B)
66
C)
D)
Find the standard form of the equation of the ellipse satisfying the given conditions.
125)
Major axis vertical with length 14; length of minor axis =12; center (0, 0)
125)
A)
B)
C)
x2
49 +y2
36 = 1
D)
Find the vertex, focus, and directrix of the parabola with the given equation.
126)
(y + 3)2=12(x + 2)
126)
A)
vertex: (2, 3)
focus: (5, 3)
directrix: x = – 1
B)
vertex: (–3, –2)
focus: (0, –2)
directrix: x = – 6
C)
vertex: (–2, –3)
focus: (–5, –3)
directrix: x =1
D)
vertex: (–2, –3)
focus: (1, –3)
directrix: x = – 5
67
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.
127)
(y –5)2= x +25
y = – 1
5x
127)
A)
B)
C)
{(–25, 5)}
D)
68
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7