104)
y2
64 –x2
4= 1
104)
A)
B)
C)
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.
105)
105)
The sum of the squares of two numbers is 90. The difference of the two numbers is 6. Find the
two numbers.
A)
3 and 9 or –9 and –3
B)
–9 and –3
C)
–9 and 3 or –3 and 9
D)
3 and 9
Sketch the ellipse for the equation.
106)
(x – 2)2+9(y + 2)2=9
106)
A)
B)
62
C)
D)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
107)
4x2=144 –4y2
107)
A)
circle
B)
parabola
63
C)
ellipse
D)
hyperbola
Solve the system by the substitution method.
108)
x2+y2=5
x + y =3
108)
A)
{(–2, 1), (–1, 2)}
B)
{(2, –1), (1, –2)}
C)
{(–2, –1), (–1, –2)}
D)
{(2, 1), (1, 2)}
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
109)
25x2=225 –y2
109)
A)
parabola
B)
ellipse
C)
circle
D)
hyperbola
Sketch the ellipse for the equation.
64
110)
(x + 2)2
9+(y – 1)2
16 = 1
110)
A)
B)
C)
D)
Solve the system by the substitution method.
111)
y =(x + 5)2+ 1
2x – y + 10 = 0
111)
A)
{(0, 10), (0, 26)}
B)
{(–5, 0)}
C)
{(–4, 2)}
D)
{(–4, 2), (4, 18)}
Graph the ellipse.
112)
9x2+4y2=36
112)
A)
B)
C)
D)
66
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
113)
y =x2+ 4x + 9
113)
A)
vertical; opens upward; (2, 5)
B)
horizontal; opens to the right; (5, 2)
C)
horizontal; opens to the right; (5, –2)
D)
vertical; opens upward; (–2, 5)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
114)
(x + 2)2+(y + 1)2=9
114)
A)
ellipse
B)
parabola
67
C)
hyperbola
D)
circle
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.
115)
115)
The sum of two numbers is 21 and their product is 108. Find the numbers.
A)
9 and –12 or –9 and 12
B)
9 and 12 or –9 and –12
C)
–9 and –12
D)
9 and 12
Determine whether the system is a nonlinear system or a linear system.
116)
4x – y = 10
x2=4y + 11
116)
A)
linear system
B)
nonlinear system
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
117)
x = – 8y2– 128y – 505
117)
A)
(7, –8)
B)
(0, –8)
C)
(7, 8)
D)
(8, 7)
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
118)
y = 2(x – 9)2+ 10
118)
A)
horizontal; opens to right; (10, –9)
B)
horizontal; opens to right; (10, 9)
C)
vertical; opens upward; (–9, 10)
D)
vertical; opens upward; (9, 10)
Solve the system by the addition method.
119)
2x2+ y2= 17
3x2– 2y2= – 6
119)
A)
{(2, –3), (–2, 3)}
B)
{(1, 3), (–1, –3)}
C)
{(2, 3), (2, –3), (–2, 3), (–2, –3)}
D)
{(1, 3), (1, –3), (–1, 3), (–1, –3)}
Write the standard form of the equation of the circle with the given center and radius.
120)
120)
Center (0, 0), r =9
A)
x2+y2=18
B)
x2–y2=9
C)
x2+y2=81
D)
x2+y2=9
Solve the problem.
121)
121)
The arch beneath a bridge is semi–elliptical, a one–way roadway passes under the arch. The
width of the roadway is 40 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 8 feet wide. Truck 1 has an overall height of
10 feet and Truck 2 has an overall height of 9 feet. Draw a rough sketch of the situation and
determine which of the trucks can pass under the bridge.
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.
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
122)
x = 2(y – 1)2+ 10
122)
A)
horizontal; opens to right; (10, –1)
B)
vertical; opens upward; (1, 10)
C)
horizontal; opens to right; (10, 1)
D)
vertical; opens upward; (–1, 10)
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
123)
x = – y2– 4y – 6
123)
70
A)
Axis of symmetry is y =2.
B)
Axis of symmetry is x =2.
C)
Axis of symmetry is x = – 2.
D)
Axis of symmetry is y = – 2.
Write the standard form of the equation of the circle with the given center and radius.
124)
124)
Center (4, 9), r =5
A)
(x + 9)2+ (y + 4)2=5
B)
(x + 4)2+ (y + 9)2=25
C)
(x – 9)2+ (y – 4)2=5
D)
(x – 4)2+ (y – 9)2=25
Solve the system by the addition method.
125)
y2+2x2=13
y2–x2= 1
125)
A)
(3, 5), (3, –5)
B)
(2, 5), (2, –5)
C)
(2, 5), (2, –5), (–2, 5), (–2, –5)
D)
(3, 5), (3, –5), (–3, 5), (–3, –5)
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
126)
y2=100 – x2
126)
A)
circle
B)
parabola
C)
hyperbola
D)
ellipse
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph
the equation.
127)
x2+y2– 10x – 4y + 4 = 0
127)
A)
(x + 5)2+(y + 2)2=25
center (–5, –2), r =5
B)
(x – 5)2+(y – 2)2=25
center (5, 2), r =5
72
C)
(x – 5)2+(y + 2)2=25
center (5, –2), r =5
D)
(x + 5)2+(y – 2)2=25
center (–5, 2), r =5
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.
128)
128)
The sum of the squares of two numbers is 45. The sum of the two numbers is 3. Find the two
numbers.
A)
–3 and 6 or –6 and 3
B)
–6 and 3
C)
–6 and –3 or 3 and 6
D)
–3 and 6
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
129)
4y2=9x2+36
129)
73
A)
ellipse
B)
circle
C)
hyperbola
D)
parabola
Solve the system by the addition method.
130)
x2+y2=4
x2–y2=4
130)
A)
{(2, 0), (–2, 0)}
B)
{(0, 2)}
C)
{(0, 2), (0, –2)}
D)
{(2, 0)}
Find the vertices of the hyperbola with the given equation.
131)
x2
1–y2
16 = 1
131)
A)
(0, –1), (0, 1)
B)
(–1, 0), (1, 0)
C)
(0, –4), (0, 4)
D)
(–4, 0), (4, 0)
Write the standard form of the equation of the circle with the given center and radius.
132)
Center (0, 0), r =11
132)
A)
x2+y2=121
B)
x2+y2=11
C)
x2+y2=5.5
D)
x2+y2=11
Find the standard form of the equation of the hyperbola.
133)
133)
A)
y2
9–x2
16 = 1
B)
x2
9–y2
16 = 1
C)
x2
16 –y2
9= 1
D)
y2
16 –x2
9= 1
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
134)
x =y2+ 2y + 4
134)
A)
(4, 0)
B)
(3, –1)
C)
(–1, 3)
D)
(0, 1)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
135)
(x + 1)2
16 +(y – 2)2
9= 1
135)
A)
ellipse
B)
hyperbola
C)
circle
D)
parabola
76
Sketch the ellipse for the equation.
136)
(x – 1)2+(y +
2)2
16 = 1
136)
A)
B)
C)
D)
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
137)
16x2=400 +16y2
137)
A)
ellipse
B)
hyperbola
C)
circle
D)
parabola
Solve the system by the substitution method.
138)
xy =6
x + y = – 5
138)
A)
{(2, 3), (3, 2)}
B)
{(–2, 3), (–3, 2)}
C)
{(2, –3), (3, –2)}
D)
{(–2, –3), (–3, –2)}
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
139)
x =5y2
139)
A)
(5, 0)
B)
(0, 0)
C)
(0, 5)
D)
(5, 5)
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
140)
x = – 1
2(y – 4)2+
2
140)
78
A)
Axis of symmetry is x = – 4.
B)
Axis of symmetry is x =4.
C)
Axis of symmetry is y =4.
D)
Axis of symmetry is y = – 4.
Sketch the ellipse for the equation.
141)
(x + 1)2
16 +(y – 2)2= 1
141)