A)
B)
C)
D)
Solve the system.
142)
4x2– 2y2= – 16
5x2+ 3y2=68
142)
A)
{(2, 4), (4, 2), (–2, –4), (–4, –2)}
B)
{(2, –4), (2, 4)}
C)
{(–2, –4), (–4, –2)}
D)
{(2, 4), (–2, 4), (2, –4), (–2, –4)}
Use vertices and asymptotes to graph the hyperbola.
80
143)
4x2–y2=36
143)
A)
B)
C)
D)
Write the standard form of the equation of the circle with the given center and radius.
144)
Center (–8, 5), r =19
144)
A)
(x – 8)2+ (y + 5)2=19
B)
(x – 5)2+ (y + 8)2=361
C)
(x + 5)2+ (y – 8)2=361
D)
(x + 8)2+ (y – 5)2=19
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
145)
x – 7 + 4y =y2
145)
A)
parabola
B)
circle
C)
hyperbola
D)
ellipse
Find the vertices of the hyperbola with the given equation.
146)
100x2=81y2+8100
146)
A)
(0, –9), (0, 9)
B)
(0, –10), (0, 10)
C)
(–10, 0), (10, 0)
D)
(–9, 0), (9, 0)
Solve the system by the addition method.
147)
x2+y2=25
x2–y2= – 7
147)
A)
{(3, –4), (3, 4)}
B)
{(3, 4), (–3, 4), (3, –4), (–3, –4)}
C)
{(–3, –4), (–4, –3)}
D)
{(3, 4), (4, 3), (–3, –4), (–4, –3)}
Solve the problem.
148)
148)
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 11
feet. Two trucks plan to use this road. They are both 12 feet wide. Truck 1 has an overall height of
11 feet and Truck 2 has an overall height of 12 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.
Find the standard form of the equation of the ellipse.
149)
149)
A)
x2
3+y2
2= 1
B)
x2
2+y2
3= 1
C)
x2
9+y2
4= 1
D)
x2
4+y2
9= 1
The equation of a parabola is given. Determine if the parabola is horizontal or vertical, the way the parabola opens, and
the vertex.
150)
y = – (x + 10)2+ 7
150)
A)
vertical; opens downward; (10, 7)
B)
horizontal; opens to left; (7, – 10)
C)
horizontal; opens to left; (7, 10)
D)
vertical; opens downward; (– 10, 7)
Determine whether the system is a nonlinear system or a linear system.
151)
y = x +5
x + y = 16
151)
A)
linear system
B)
nonlinear system
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola‘s axis of symmetry.
152)
x =2(y + 3)2– 1
152)
A)
Axis of symmetry is y =3.
B)
Axis of symmetry is x = – 3.
84
C)
Axis of symmetry is y = – 3.
D)
Axis of symmetry is x =3.
Solve the system by the substitution method.
153)
y = x + 4
y2=16x
153)
A)
{(4, 8)}
B)
{(4, 8), (–4, 0)}
C)
{(4, 8), (4, –8), (–4, 0)}
D)
{(4, 8), (4, –8)}
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.
154)
154)
The difference between the squares of two numbers is 28. Twice the square of the second number
subtracted from the square of the first number is –8. Find the numbers.
A)
8 and 6, –8 and 6, or 8 and –6
B)
8 and 6
C)
8 and 6 or –8 and –6
D)
8 and 6, –8 and 6, 8 and –6, or –8 and –6
The equation of a horizontal parabola is given. Determine how the parabola opens and find the parabola’s vertex.
155)
x = – (y + 1)2– 4
155)
A)
opens to left; (–4, 1)
B)
opens to left; (–4, –1)
C)
opens to right; (–1, –4)
D)
opens to left; (–1, –4)
Solve the system by the addition method.
156)
2x2+ y2= 66
x2+ y2= 41
156)
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)}
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
157)
x = – y2– 6y
157)
A)
circle
B)
hyperbola
86
C)
ellipse
D)
parabola
Solve the system by the addition method.
158)
x2–y2=7
x2+y2=31
158)
A)
{( 19, 2 3), (–19, 2 3), ( 19, –2 3), (–19, –2 3)}
B)
{( 19, 2 3), (–19, –2 3)}
C)
{(0, 0)}
D)
{( 19, 2 3), (–19, 2 3)}
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola‘s axis of symmetry.
159)
x =1
2y2– 3y +11
2
159)
87
A)
Axis of symmetry is y =3.
B)
Axis of symmetry is x = – 3.
C)
Axis of symmetry is y = – 3.
D)
Axis of symmetry is x =3.
Find the standard form of the equation of the ellipse.
160)
160)
A)
x2
36 +y2= 1
B)
x2
6+y2= 1
C)
x2+y2
36 = 1
D)
x2+y2
6= 1
Sketch the ellipse for the equation.
161)
9(x + 2)2+16(y – 1)2=144
161)
A)
B)
89
C)
D)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
162)
x2=64 –(y +5)2
162)
A)
ellipse
B)
hyperbola
90
C)
circle
D)
parabola
163)
3x2=48 –y2
163)
A)
ellipse
B)
parabola
91
C)
hyperbola
D)
circle
Find the vertices of the hyperbola with the given equation.
164)
64x2–100y2=6400
164)
A)
(–8, 0), (8, 0)
B)
(0, –8), (0, 8)
C)
(–10, 0), (10, 0)
D)
(0, –10), (0, 10)
Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph
the equation.
165)
x2+y2– 4x + 8y + 11 = 0
165)
92
A)
(x + 2)2+(y – 4)2=9
center (–2, 4), r =3
B)
(x + 2)2+(y + 4)2=9
center (–2, –4), r =3
C)
(x – 2)2+(y – 4)2=9
center (2, 4), r =3
D)
(x – 2)2+(y + 4)2=9
center (2, –4), r =3
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
166)
x =(y – 2)2+ 1
166)
A)
(1, 2)
B)
(2, 1)
C)
(–2, 1)
D)
(1, –2)
Give the center and radius of the circle described by the equation and graph the equation.
93
167)
(x +4)2+(y +5)2=25
167)
A)
center (–4, 5), r =5
B)
center (4, –5), r =5
C)
center (4, 5), r =5
D)
center (–4, –5), r =5
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
94
168)
x =(y – 2)2+ 1
168)
A)
circle
B)
ellipse
C)
hyperbola
D)
parabola
Use vertices and asymptotes to graph the hyperbola.
95
169)
36x2–9y2=324
169)
A)
B)
C)
D)
Solve the problem.
170)
170)
A local university is building a new arena to hold basketball games, indoor track meets, concerts,
etc. The arena will be elliptical in shape with external dimensions of 470 feet by 380 feet. Assume
that the center of the arena is the origin. Write an equation that models the shape of the new
arena.
A)
x2
1902+y2
2352= 1
B)
x2
3802+y2
4702= 1
C)
x2
4702+y2
3802= 1
D)
x2
2352+y2
1902= 1