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120)
(x +5)2+(y +4)2=25
120)
A)
center (-5, 4), r =5
B)
center (-5, -4), r =5
C)
center (5, 4), r =5
D)
center (5, -4), r =5
Solve the problem.
121)
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width
of the roadway is 32 feet and the height of the arch over the center of the roadway is 11 feet. Two
trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of 10 feet and
Truck 2 has an overall height of 11 feet. Draw a rough sketch of the situation and determine which
of the trucks can pass under the bridge.
121)
A)
Truck 1 can pass under the bridge, but Truck 2 cannot.
B)
Truck 2 can pass under the bridge, but Truck 1 cannot.
C)
Both Truck 1 and Truck 2 can pass under the bridge.
D)
Neither Truck 1 nor Truck 2 can pass under the bridge.
Solve the system by the addition method.
122)
2x2+ y2= 17
3x2- 2y2= - 6
122)
A)
{(1, 3), (1, -3), (-1, 3), (-1, -3)}
B)
{(1, 3), (-1, -3)}
C)
{(2, -3), (-2, 3)}
D)
{(2, 3), (2, -3), (-2, 3), (-2, -3)}
Give the center and radius of the circle described by the equation and graph the equation.
123)
(x -5)2+(y -3)2=4
123)
62
A)
center (5, 3), r =2
B)
center (-5, 3), r =2
C)
center (5, -3), r =2
D)
center (-5, -3), r =2
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
124)
x2
36 +y2
36 = 1
124)
63
A)
ellipse
B)
circle
C)
hyperbola
D)
parabola
Provide an appropriate response.
125)
Find the distance between (-5, 6) and (3, -3). Give an exact answer.
125)
A)
72 units
B)
145 units
C)
17 units
D)
145 units
Solve the system by the addition method.
126)
x2+y2- 4x - 2y - 11 = 0
x2-y2- 4x + 2y - 13 = 0
126)
A)
{(2, -5), (2, 3)}
B)
{(6, 1), (2, 1)}
C)
{(2, 5), (2, -3)}
D)
{(6, 1), (-2, 1)}
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
127)
x - 9 + 6y =3y2
127)
A)
circle
B)
ellipse
C)
hyperbola
D)
parabola
Find the standard form of the equation of the ellipse.
128)
128)
A)
x2+y2
10 = 1
B)
x2
10 +y2= 1
C)
x2
100 +y2= 1
D)
x2+y2
100 = 1
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
129)
9x2=36 +y2
129)
A)
parabola
B)
ellipse
C)
circle
D)
hyperbola
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola's axis of symmetry.
65
130)
x =y2- 12y + 40
130)
A)
Axis of symmetry is x =6.
B)
Axis of symmetry is y = - 6.
C)
Axis of symmetry is y =6.
D)
Axis of symmetry is x = - 6.
66
Find the distance between the pair of points. Give an exact answer.
131)
(-2, -2) and (4, -4)
131)
A)
32 2 units
B)
8 units
C)
32 units
D)
210 units
Use vertices and asymptotes to graph the hyperbola.
132)
36y2-4x2=144
132)
A)
B)
C)
D)
D)
Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear
equations. Solve the system and find the numbers.
133)
The sum of the squares of two numbers is 41. The difference of the two numbers is 1. Find the two
numbers.
133)
A)
4 and 5 or -5 and -4
B)
4 and 5
C)
-4 and 5 or -5 and 4
D)
-5 and -4
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the
equation.
134)
x2+y2- 8x - 8y + 23 = 0
134)
A)
(x - 4)2+(y + 4)2=9
center (4, -4), r =3
B)
(x - 4)2+(y - 4)2=9
center (4, 4), r =3
68
C)
(x + 4)2+(y + 4)2=9
center (-4, -4), r =3
D)
(x + 4)2+(y - 4)2=9
center (-4, 4), r =3
Solve the problem.
135)
A rectangular coordinate system with coordinates in miles is placed with the origin at the center of
Los Angeles. A university is located 34.9 miles east and 50.9 miles north of central Los Angeles. A
seismograph on the campus shows a small earthquake occurred. The quake's epicenter is 26.9 miles
from the university. Write the standard form of the equation for the set of points that could be the
epicenter of the quake.
135)
A)
(x -34.9)2+(y -50.9)2=26.9
B)
(x +34.9)2+(y +50.9)2=723.61
C)
(x -34.9)2+(y -50.9)2=723.61
D)
(x +34.9)2+(y +50.9)2=26.9
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
136)
x = - 6y2- 96y - 379
136)
A)
(0, -8)
B)
(5, 8)
C)
(5, -8)
D)
(8, 5)
Find the standard form of the equation of the ellipse.
137)
137)
A)
x2
8+y2
6= 1
B)
x2
36 +y2
64 = 1
C)
x2
64 +y2
36 = 1
D)
x2
6+y2
8= 1
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
138)
x2=384 -6(y +6)2
138)
A)
circle
B)
hyperbola
70
C)
parabola
D)
ellipse
Graph the ellipse.
139)
x2
25 +y2
16 = 1
139)
A)
B)
71
C)
D)
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the
equation.
140)
x2+y2+ 6x + 8y + 21 = 0
140)
A)
(x + 3)2+(y + 4)2=4
center (-3, -4), r =2
B)
(x + 3)2+(y - 4)2=4
center (-3, 4), r =2
72
C)
(x - 3)2+(y - 4)2=4
center (3, 4), r =2
D)
(x - 3)2+(y + 4)2=4
center (3, -4), r =2
Give the coordinates for the vertex for the parabola.
141)
x = - 2(y + 5)2- 8
141)
A)
(-5, -8)
B)
(-8, 5)
C)
(-8, -5)
D)
(5, -8)
Solve the system by the substitution method.
142)
y =(x + 5)2+ 1
2x - y + 10 = 0
142)
A)
{(-5, 0)}
B)
{(-4, 2)}
C)
{(-4, 2), (4, 18)}
D)
{(0, 10), (0, 26)}
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the
equation.
73
143)
x2+y2- 16x + 63 = 0
143)
A)
x2+(y - 8)2=1
center (0, 8), r =1
B)
(x + 8)2+y2=1
center (-8, 0), r =1
C)
(x - 8)2+y2=1
center (8, 0), r =1
D)
x2+(y + 8)2=1
center (0, -8), r =1
74
Solve the system by the addition method.
144)
x2+y2=64
x2-y2=64
144)
A)
{(8, 0)}
B)
{(0, 8), (0, -8)}
C)
{(8, 0), (-8, 0)}
D)
{(0, 8)}
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
145)
25x2+9y2=225
145)
A)
ellipse
B)
circle
C)
parabola
D)
hyperbola
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola's axis of symmetry.
146)
x = - 2(y - 2)2+ 4
146)
A)
Axis of symmetry is x = - 2.
B)
Axis of symmetry is x =2.
C)
Axis of symmetry is y = - 2.
D)
Axis of symmetry is y =2.
76
Write the standard form of the equation of the circle with the given center and radius.
147)
Center (6, 0), r =5
147)
A)
x2+ (y + 6)2=5
B)
x2+ (y - 6)2=5
C)
(x + 6)2+ y2=25
D)
(x - 6)2+ y2=25
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
148)
x =9y2
148)
A)
(0, 0)
B)
(9, 9)
C)
(0, 9)
D)
(9, 0)
Solve the problem.
149)
A system for tracking ships indicated that a ship lies on a hyperbolic path described by
6x2-y2=135. The process is repeated and the ship is found to lie on a hyperbolic path described
by y2-2x2=9. If it is known that the ship is located in the first quadrant of the coordinate system,
determine its exact location.
149)
A)
(9, 6)
B)
(-6, -9)
C)
(6, 9)
D)
(-9, -6)
Find the distance between the pair of points. Give an exact answer.
150)
(-1, -3) and (-9, -9)
150)
A)
10 units
B)
20 units
C)
11 units
D)
100 units
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
151)
x = - y2- 2y + 4
151)
A)
horizontal; opens to the left; (5, 1)
B)
vertical; opens downward; (1, 5)
C)
vertical; opens downward; (-1, 5)
D)
horizontal; opens to the left; (5, -1)
77
Solve the system by the addition method.
152)
x2+y2=9
9x2+4y2=36
152)
A)
{(2, 0), (-2, 0)}
B)
{(3, 0), (-3, 0)}
C)
{(0, 3), (0, -3)}
D)
{(0, 2), (0, -2)}
Find the distance between the pair of points. Give an exact answer.
153)
(-5, -3) and (3, -5)
153)
A)
60 15 units
B)
217 units
C)
10 units
D)
60 units
Use vertices and asymptotes to graph the hyperbola.
154)
x2-9y2=36
154)
A)
B)
78
C)
D)
Solve the system by the addition method.
155)
2x2- 2y2= - 14
3x2+ 3y2=75
155)
A)
{(3, 4), (-3, 4), (3, -4), (-3, -4)}
B)
{(-3, -4), (-4, -3)}
C)
{(3, -4), (3, 4)}
D)
{(3, 4), (4, 3), (-3, -4), (-4, -3)}
Use vertices and asymptotes to graph the hyperbola.
156)
y2
16 -x2
9= 1
156)
79
A)
B)
C)
D)
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the
equation.
157)
x2+y2- 14y + 48 = 0
157)
80
