A)
circle
B)
ellipse
C)
hyperbola
D)
parabola
Sketch the ellipse for the equation.
83)
9(x – 1)2+(y + 2)2=9
83)
41
A)
B)
C)
D)
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
84)
x =(y + 2)2– 1
84)
A)
(2, –1)
B)
(–1, 2)
C)
(–1, –2)
D)
(–2, –1)
Sketch the ellipse for the equation.
42
85)
16(x – 1)2+9(y + 2)2=144
85)
A)
B)
C)
D)
43
Provide an appropriate response.
86)
Find the midpoint of the line segment whose endpoints are (–6, –6) and (2, 8).
86)
A)
– 2, 1
B)
(–4, 2)
C)
– 4, – 7
D)
(–8, –14)
Find the standard form of the equation of the ellipse.
87)
87)
A)
x2
49 +y2= 1
B)
x2+y2
7= 1
C)
x2+y2
49 = 1
D)
x2
7+y2= 1
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
88)
5x2=45 +5y2
88)
44
A)
hyperbola
B)
ellipse
C)
circle
D)
parabola
Determine whether the system is a nonlinear system or a linear system.
89)
y = x +5
x + y = 16
89)
A)
nonlinear system
B)
linear system
B
A
Solve the problem.
90)
The arch beneath a bridge is semi–elliptical, a one–way roadway passes under the arch. The width
of the roadway is 30 feet and the height of the arch over the center of the roadway is 12 feet. Two
trucks plan to use this road. They are both 8 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.
90)
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.
Find the vertices of the hyperbola with the given equation.
91)
y2
64 –x2
9= 1
91)
A)
(–8, 0), (8, 0)
B)
(0, –8), (0, 8)
C)
(0, –3), (0, 3)
D)
(–3, 0), (3, 0)
B
Determine whether the system is a nonlinear system or a linear system.
92)
y =x2+8
x2+y2= 16
92)
A)
nonlinear system
B)
linear system
A
Solve the system by the addition method.
93)
2x2+ y2= 66
x2+ y2= 41
93)
A)
{(4, 5), (–4, 5), (4, –5), (–4, –5)}
B)
{(4, 5), (–4, –5)}
C)
{(5, 4), (–5, –4)}
D)
{(5, 4), (5, –4), (–5, 4), (–5, –4)}
D
D
Determine whether the system is a nonlinear system or a linear system.
94)
4x – y = 10
x =6y + 11
94)
A)
linear system
B)
nonlinear system
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
95)
16x2=400 +16y2
95)
A)
circle
B)
ellipse
C)
parabola
D)
hyperbola
D
D)
Sketch the ellipse for the equation.
96)
(x + 1)2
16 +(y + 2)2= 1
96)
A)
B)
47
A
C)
D)
Find the standard form of the equation of the hyperbola.
97)
97)
A)
y2
16 –x2
4= 1
B)
x2
16 –y2
4= 1
C)
y2
4–x2
16 = 1
D)
x2
4–y2
16 = 1
Solve the system by the substitution method.
98)
x – 2y = 3
x2– xy = 20
98)
A)
(5, 1), –8, –11
2
B)
(5, 1), –11
2, –8
C)
(–5, –1), 8, 11
2
D)
(–5, –1), 11
2, 8
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
99)
x = – y2+ 2y
99)
A)
hyperbola
B)
circle
49
C)
parabola
D)
ellipse
Find the vertices of the hyperbola with the given equation.
100)
144x2–81y2=11,664
100)
A)
(0, –9), (0, 9)
B)
(0, –12), (0, 12)
C)
(–9, 0), (9, 0)
D)
(–12, 0), (12, 0)
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
101)
x – 5 – 6y =y2
101)
A)
circle
B)
parabola
C)
hyperbola
D)
ellipse
Solve the problem.
102)
The rectangular plot of land shown in the figure is to be fenced along three sides using 55 feet of
fencing. No fencing is to be placed along the river’s edge. The area of the plot is 300 square feet.
What are its dimensions?
102)
A)
40 ft by 7.5 ft
B)
15 ft by 20 ft
C)
30 ft by 10 ft or 40 ft by 7.5 ft
D)
15 ft by 20 ft or 40 ft by 7.5 ft
Graph the ellipse.
103)
x2+5y2=20
103)
A)
B)
51
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.
104)
The sum of the squares of two numbers is 13. The sum of the two numbers is 1. Find the two
numbers.
104)
A)
–3 and –2 or 2 and 3
B)
–2 and 3 or –3 and 2
C)
–2 and 3
D)
–3 and 2
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
105)
4y2=64 +4x2
105)
A)
circle
B)
hyperbola
C)
ellipse
D)
parabola
Graph the ellipse.
52
106)
x2
4+y2
25 = 1
106)
A)
B)
C)
D)
Find the midpoint of the line segment with the given end points.
107)
(2, 9) and (4, 8)
107)
A)
(–2, 1)
B)
(6, 17)
C)
– 1, 1
2
D)
3, 17
2
Write the standard form of the equation of the circle with the given center and radius.
108)
Center (0, 0), r =2
108)
A)
x2+y2=1
B)
x2+y2=2
C)
x2+y2=4
D)
x2+y2=2
B
Solve the system by the addition method.
109)
x2– 3y2– 1 = 0
4x2+ 3y2– 19 = 0
109)
A)
{(–1, 2), (1, –2)}
B)
{(1, 2), (–1, 2), (1, –2), (–1, –2)}
C)
{(2, 1), (–2, –1)}
D)
{(2, 1), (2, –1), (–2, 1), (–2, –1)}
D
Give the center and radius of the circle.
110)
(x + 7)2+ (y + 10)2=121
110)
A)
center: (7, 10); r =121
B)
center: (7, 10); r =11
C)
center: (–7, –10); r =11
D)
center: (–7, –10); r =121
C
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
54
D
111)
x =2y2– 16y + 33
111)
A)
Axis of symmetry is y =4.
B)
Axis of symmetry is x =4.
C)
Axis of symmetry is y = – 4.
D)
Axis of symmetry is x = – 4.
55
Solve the system by the substitution method.
112)
x + y =5
y =x2– 10x + 25
112)
A)
{(–4, 9), (–5, 10)}
B)
{(5, 0)}
C)
{(4, 1), (5, 0)}
D)
{(4, 9), (5, 0)}
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 = 2(x – 1)2– 7
113)
A)
vertical; opens upward; (1, –7)
B)
horizontal; opens to right; (–7, –1)
C)
horizontal; opens to right; (–7, 1)
D)
vertical; opens upward; (–1, –7)
A
Write the standard form of the equation of the circle with the given center and radius.
114)
Center (1, 4), r =3
114)
A)
(x + 4)2+ (y + 1)2=3
B)
(x – 4)2+ (y – 1)2=3
C)
(x + 1)2+ (y + 4)2=9
D)
(x – 1)2+ (y – 4)2=9
D
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the
equation.
115)
x2+y2+ 6x – 12y + 36 = 0
115)
56
C
A)
(x – 3)2+(y – 6)2=9
center (3, 6), r =3
B)
(x + 3)2+(y + 6)2=9
center (–3, –6), r =3
C)
(x – 3)2+(y + 6)2=9
center (3, –6), r =3
D)
(x + 3)2+(y – 6)2=9
center (–3, 6), r =3
Solve the problem.
116)
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 9 feet. Two
trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of 9 feet and
Truck 2 has an overall height of 8 feet. Draw a rough sketch of the situation and determine which
of the trucks can pass under the bridge.
116)
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.
Sketch the ellipse for the equation.
57
117)
(x – 1)2+16(y + 1)2=16
117)
A)
B)
C)
D)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
58
118)
(x + 2)2+(y + 1)2=16
118)
A)
hyperbola
B)
ellipse
C)
circle
D)
parabola
Sketch the ellipse for the equation.
59
119)
(x – 2)2+(y + 2)2
9= 1
119)
A)
B)
C)
D)
Give the center and radius of the circle described by the equation and graph the equation.
60