A)
B)
C)
D)
Is the relation a function?
77)
y2– 10y – x + 24 = 0
A)
Yes
B)
No
Find the standard form of the equation of the ellipse satisfying the given conditions.
78)
Foci: (–3, 0), (3, 0); vertices: (–4, 0), (4, 0)
A)
x2
9+y2
7= 1
B)
x2
9+y2
16 = 1
C)
x2
16 +y2
7= 1
D)
x2
7+y2
16 = 1
Find the standard form of the equation of the hyperbola satisfying the given conditions.
79)
Foci: (–10, 0), (10, 0); vertices: (–4, 0), (4, 0)
A)
y2
16 –x2
100 = 1
B)
y2
16 –x2
84 = 1
C)
x2
16 –y2
100 = 1
D)
x2
16 –y2
84 = 1
Convert the equation to the standard form for a hyperbola by completing the square on x and y.
80)
9x2–16y2+ 18x – 32y – 151 = 0
A)
(x + 1)2
9–(y + 1)2
16 = 1
B)
(x + 1)2
16 –(y – 1)2
9= 1
C)
(x – 1)2
16 –(y + 1)2
9= 1
D)
(x + 1)2
16 –(y + 1)2
9= 1
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.
81)
x =y2–7
x =y2–7y
A)
{(1, –6)}
B)
{(6, 1)}
C)
{(–6, 1)}
D)
{(–6, –1)}
Find the standard form of the equation of the hyperbola satisfying the given conditions.
82)
Foci: (0, –9), (0, 9); vertices: (0, –7), (0, 7)
A)
y2
49 –x2
81 = 1
B)
x2
49 –y2
81 = 1
C)
x2
49 –y2
32 = 1
D)
y2
49 –x2
32 = 1
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
83)
y2
9–x2
25 = 1
A)
Asymptotes: y = ± 5
3x
B)
Asymptotes: y = ± 3
5x
43
C)
Asymptotes: y = ± 5
3x
D)
Asymptotes: y = ± 3
5x
Find the focus and directrix of the parabola with the given equation.
84)
x =7y2
A)
focus: ( 1
28 , 0)
directrix: x =1
28
B)
focus: (0, 1
28 )
directrix: y = – 1
28
C)
focus: ( 1
28 , 0)
directrix: x = – 1
28
D)
focus: ( 1
7, 0)
directrix: x = – 1
7
Use the center, vertices, and asymptotes to graph the hyperbola.
85)
(y + 2)2
9–(x – 1)2
16 = 1
44
A)
B)
C)
D)
Graph the parabola.
86)
y2+16x = 0
45
A)
B)
C)
D)
Find the standard form of the equation of the ellipse satisfying the given conditions.
87)
Endpoints of major axis: (–7, 4) and (9, 4); endpoints of minor axis: (1, 6) and (1, 2)
A)
(x – 4)2
4+(y – 1)2
64 = 1
B)
(x – 1)2
64 +(y – 4)2
4= 1
C)
(x + 1)2
64 +(y + 2)2
4= 0
D)
(x + 1)2
64 +(y + 2)2
4= 1
Use the vertex and the direction in which the parabola opens to determine the relation’s domain and range.
88)
x = – (y + 6)2– 10
A)
Domain: (–, )
Range: (–, )
B)
Domain: (–, )
Range: (–, –10]
C)
Domain: (–, –10)
Range: (–, )
D)
Domain: (–, –10]
Range: (–, )
Use the relation’s graph to determine its domain and range.
89)
x2
4–y2
36 = 1
A)
Domain: (–, )
Range: (–, –2) or (2, )
B)
Domain: (–, –2] or [2, )
Range: (–, )
C)
Domain: (–, –2] and [2, )
Range: (–, )
D)
Domain: (–, )
Range: (–, )
Solve the problem.
90)
A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 4) and then
moves closer and closer to the line y =12
5x as it gets farther from the tracking station at the origin.
Find the equation that describes the path of the satellite if the center of the hyperbola is at (0, 0).
(0, 4)
y =12
5x
A)
y2
25
9
–x2
16 = 1
B)
y2
16 –x2
25
9
= 1
C)
x2
(36
5)2–y2
16 = 1
D)
x2
16 –y2
(36
5)2= 1
Graph the ellipse.
91)
4(x – 1)2+9(y + 1)2=36
48
A)
B)
C)
D)
Find the standard form of the equation of the ellipse satisfying the given conditions.
92)
Foci: (0, –3), (0, 3); vertices: (0, –7), (0, 7)
A)
x2
9+y2
49 = 1
B)
x2
49 +y2
40 = 1
C)
x2
40 +y2
49 = 1
D)
x2
9+y2
40 = 1
Graph the parabola with the given equation.
49
93)
(y + 2)2=6(x + 2)
A)
B)
C)
D)
Graph the ellipse and locate the foci.
50
94)
x2
11 +y2
36 = 1
A)
foci at (0, 6) and (0, –6)
B)
foci at (5, 0) and (–5, 0)
C)
foci at (0, 5) and (0, –5)
D)
foci at (0, 11) and (0, –11)
Solve the problem.
95)
Two recording devices are set 2200 feet apart, with the device at point A to the west of the device at
point B. At a point on a line between the devices, 200 feet from point B, a small amount of explosive
is detonated. The recording devices record the time the sound reaches each one. How far directly
north of site B should a second explosion be done so that the measured time difference recorded by
the devices is the same as that for the first detonation?
A)
444.44 feet
B)
1081.67 feet
C)
3420.53 feet
D)
998.76 feet
Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
96)
x2+ 2x + 6y – 11 = 0
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)
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
97)
4x2–9y2=36
A)
Asymptotes: y = ± 3
2x
B)
Asymptotes: y = ± 2
3x
52
C)
Asymptotes: y = ± 2
3x
D)
Asymptotes: y = ± 3
2x
Use the vertex and the direction in which the parabola opens to determine the relation’s domain and range.
98)
y =x2– 8x + 14
A)
Domain: [–2, )
Range: (–, )
B)
Domain: (–, )
Range: [–2, )
C)
Domain: (–, )
Range: (–2, )
D)
Domain: (–2, )
Range: (–, )
Solve the problem.
99)
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?
A)
90 miles from the master station, (136.1, 100)
B)
90 miles from the master station, (100, 136.1)
C)
36 miles from the master station, (100, 136.1)
D)
36 miles from the master station, (136.1, 100)
Find the vertex, focus, and directrix of the parabola with the given equation.
100)
(x + 1)2=16(y + 3)
100)
A)
vertex: (–1, –3)
focus: (–1, –7)
directrix: x =1
B)
vertex: (–3, –1)
focus: (–3, 3)
directrix: y = – 5
C)
vertex: (–1, –3)
focus: (–1, 1)
directrix: y = – 7
D)
vertex: (1, 3)
focus: (1, 7)
directrix: y = – 1
Solve the problem.
101)
The arch beneath a bridge is semi–elliptical, a one–way roadway passes under the arch. The width
of the roadway is 38 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 12 feet and
Truck 2 has an overall height of 13 feet. Draw a rough sketch of the situation and determine which
of the trucks can pass under the bridge.
101)
A)
Both Truck 1 and Truck 2 can pass under the bridge.
B)
Truck 2 can pass under the bridge, but Truck 1 cannot.
C)
Truck 1 can pass under the bridge, but Truck 2 cannot.
D)
Neither Truck 1 nor Truck 2 can pass under the bridge.
Find the vertex, focus, and directrix of the parabola with the given equation.
102)
(y + 3)2=12(x + 2)
102)
A)
vertex: (–3, –2)
focus: (0, –2)
directrix: x = – 6
B)
vertex: (–2, –3)
focus: (–5, –3)
directrix: x =1
C)
vertex: (2, 3)
focus: (5, 3)
directrix: x = – 1
D)
vertex: (–2, –3)
focus: (1, –3)
directrix: x = – 5
Use the center, vertices, and asymptotes to graph the hyperbola.
54
103)
(x + 1)2
4–(y – 1)2
16 = 1
103)
A)
B)
C)
D)
Find the foci of the ellipse whose equation is given.
104)
36(x – 3)2+25(y + 1)2=900
104)
A)
foci at (3, –1–11) and (3, –1+11)
B)
foci at (4, –1–11) and (4, –1+11)
C)
foci at (–3, –1–11) and (–3, –1+11)
D)
foci at (–1, 3–11) and (–1, 3+11)
Use the center, vertices, and asymptotes to graph the hyperbola.
105)
(x – 1)2–4(y – 2)2=4
105)
A)
B)
C)
D)