A)
x2+(y – 7)2=1
center (0, 7), r =1
B)
(x – 7)2+y2=1
center (7, 0), r =1
C)
(x + 7)2+y2=1
center (–7, 0), r =1
D)
x2+(y + 7)2=1
center (0, –7), r =1
Solve the system by the substitution method.
158)
x2+y2=41
x + y = – 9
158)
A)
{(–4, –5), (–5, –4)}
B)
{(–4, 5), (–5, 4)}
C)
{(4, –5), (5, –4)}
D)
{(4, 5), (5, 4)}
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
81
159)
x = – 2(y + 3)2– 3
159)
A)
Axis of symmetry is x =3.
B)
Axis of symmetry is y = – 3.
C)
Axis of symmetry is y =3.
D)
Axis of symmetry is x = – 3.
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
82
160)
4x2=64 –4y2
160)
A)
hyperbola
B)
circle
C)
ellipse
D)
parabola
83
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
161)
x2=100 –4y2
161)
A)
parabola
B)
circle
C)
hyperbola
D)
ellipse
Solve the system by the substitution method.
162)
xy = 1
–18x – y =9
162)
A)
{(3, –3), (6, –6)}
B)
–3, –1
3, –6, –1
6
C)
–1
6, –6
D)
–1
3, –3, –1
6, –6
Graph the ellipse.
163)
3x2+y2=18
163)
A)
B)
84
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.
164)
x2+y2– 4x + 10y + 25 = 0
164)
A)
(x – 2)2+(y + 5)2=4
center (2, –5), r =2
B)
(x – 2)2+(y – 5)2=4
center (2, 5), r =2
85
C)
(x + 2)2+(y + 5)2=4
center (–2, –5), r =2
D)
(x + 2)2+(y – 5)2=4
center (–2, 5), r =2
Find the distance between the pair of points. Round to the nearest thousandth.
165)
1
2, 1
7 and 3
4, 8
7
165)
A)
0.250 units
B)
4 units
C)
1.031 units
D)
0.970 units
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
166)
x2=4–(y +3)2
166)
86
A)
circle
B)
ellipse
C)
hyperbola
D)
parabola
Solve the system by the substitution method.
167)
2y – x =10
x2+y2–100 = 0
167)
A)
0, 5, 8, 9
B)
0, 5, 0, – 5 , 8, 9
C)
{(10, 0), (–10, 0), (6, 8)}
D)
{(–10, 0), (6, 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.
168)
The difference between the squares of two numbers is 9. Twice the square of the second number
subtracted from the square of the first number is –7. Find the numbers.
168)
A)
5 and 4, –5 and 4, or 5 and –4
B)
5 and 4, –5 and 4, 5 and –4, or –5 and –4
C)
5 and 4
D)
5 and 4 or –5 and –4
Find the standard form of the equation of the ellipse.
169)
169)
A)
x2
8+y2
7= 1
B)
x2
64 +y2
49 = 1
C)
x2
49 +y2
64 = 1
D)
x2
7+y2
8= 1
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
170)
y2=100 – x2
170)
A)
ellipse
B)
circle
C)
parabola
D)
hyperbola
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.
171)
The sum of two squares of two numbers is 106, and the difference of their squares is 56. Find the
numbers.
171)
A)
9 and 5, –9 and 5, or 9 and –5
B)
9 and 5, –9 and 5, 9 and –5, or –9 and –5
C)
9 and 5 or –9 and –5
D)
9 and 5
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
172)
9x2=225 –9y2
172)
A)
parabola
B)
ellipse
C)
hyperbola
D)
circle
Find the vertices of the hyperbola with the given equation.
173)
x2
64 –y2
49 = 1
173)
A)
(–7, 0), (7, 0)
B)
(–8, 0), (8, 0)
C)
(0, –7), (0, 7)
D)
(0, –8), (0, 8)
Give the center and radius of the circle described by the equation and graph the equation.
174)
x2+ y2=4
174)
89
A)
center (0, 0), r =2
B)
center (1, 1), r =2
C)
center (1, 1), r =2
D)
center (0, 0), r =2
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
175)
x =y2+ 6y + 13
175)
A)
(13, 0)
B)
(0, 3)
C)
(4, –3)
D)
(–3, 4)
Give the center and radius of the circle described by the equation and graph the equation.
90
176)
(x –3)2+(y +2)2=9
176)
A)
center (–3, 2), r =3
B)
center (–3, –2), r =3
C)
center (3, 2), r =3
D)
center (3, –2), r =3
Graph the ellipse.
91