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Precalculus
Unit 8 – Conics
Name
Date
Tuesday April 5, 2016
Homework: Circles #1
Find the center and radius of each circle.
1.
( x − 7 ) + ( y − 2)
4.
( x + 5) + ( y − 1)
2
2
2
2
=
64
2.
( x + 6 ) + ( y + 3)
=
24
5.
( x − 3)
2
2
2
+ y2 =
19
=
81
3.
( x − 8) + ( y + 5)
6.
3
2
x2 + ( y + 4) =
4
2
2
=
10
Write an equation for a circle with the given center and radius.
7.
center = ( −2, 6 ) radius =
9.
center = ( 4, −2 ) radius = 3 5
11.
What is the greatest y-coordinate among all points on the circle ( x + 4 ) + ( y − 6 ) =
9?
B. 9
10.
center = ( 0, 0 ) radius =
C. 5
1
3
15
2
D. 3
2
(−
2, 2
)
G.
( −2, 2 )
E. -3
H.
(
2, − 2
2
)
J.
( 2, −2 )
K.
( 2, 2 )
In the ( x, y ) coordinate plane, what is the radius of the circle ( x − 2 ) + ( y + 1) =
6?
2
A. 1
14.
center = ( 7, 0 ) radius = 2
What is the center of the circle with equation ( x − 2 ) + ( y + 2 ) =
2 in the standard ( x, y ) coordinate plane?
12.
13.
8.
2
A. 15
F.
3
5
B.
2
2
C. 2
D.
E. 6
6
One of the following is an equation for a circle, centered at C and passing through the origin in the standard
( x, y ) coordinate plane below. Point C is 3 coordinate units from the y-axis and 4 from the x-axis. Which
equation determines the circle?
A.
B.
C.
D.
E.
25
( x + 4 ) + ( y + 3) =
2
2
25
( x + 4 ) + ( y − 3) =
2
2
25
( x + 3) + ( y − 4 ) =
2
2
25
( x − 3) + ( y + 4 ) =
2
2
25
( x − 4 ) + ( y + 3) =
2
8
2
6
C
4
2
-5
O
Which of the following is an equation of the circle that has its center at C ( 2,3) and passes through A ( 5, 7 )
15.
in the standard ( x, y ) coordinate plane?
A.
B.
5
( x − 2 ) + ( y − 3) =
2
2
25
( x − 2 ) + ( y − 3) =
2
B.
C.
D.
29
( x − 2 ) + ( y − 3) =
2
2
29
( x − 5 ) + ( y − 3) =
2
2
( x − 5)
E.
2
+ ( y − 7) =
25
2
Which of the following is an equation for the circle in the standard ( x, y ) plane: center at ( 2,3) and radius 3?
16.
A.
2
9
( x − 2 ) + ( y + 3) =
2
2
9
( x + 3) + ( y + 2 ) =
2
2
C.
D.
9
( x − 2 ) + ( y − 3) =
2
2
3
( x − 2 ) + ( y + 3) =
2
2
( x − 2)
E.
2
+ ( y − 3) =
3
2
Which of the following is an equation of the circle in the standard ( x, y ) coordinate plane below?
17.
y
6
A.
B.
C.
( x − 3) + ( y + 3) =3
2
2
6
( x + 3) + ( y − 3) =
2
2
6
( x − 3) + ( y + 3) =
2
2
D.
E.
9
( x + 3) + ( y − 3) =
2
2
9
( x − 3) + ( y + 3) =
2
2
4
( 0,3 )
2
-5
(-3, 0)
x
In the standard ( x, y ) coordinate plane, the center of the circle shown below lies on the x-axis at x = 4. If the
18.
circle is tangent to the y-axis, which of the following is an equation of the circle?
y
A.
B.
C.
4
( x + 4) + y =
2
16
( x − 4) + y2 =
2
16
( x − 4) − y2 =
2
2
D.
E.
4
( x − 4) + y =
2
x2 + ( y − 4) =
16
2
2
4
x
A circle in the standard ( x, y ) coordinate plane has a center ( 2, −3) and radius 4 units. Which of the
19.
following equations represents this circle?
A.
B.
C.
20.
4
( x − 2 ) + ( y + 3) =
2
2
4
( x + 2 ) − ( y − 3) =
2
2
4
( x + 2 ) + ( y − 3) =
2
2
D.
E.
16
( x − 2 ) + ( y + 3) =
2
2
16
( x + 2 ) − ( y − 3) =
2
2
Which of the following graphs in the standard coordinate plane represents the equation
x2 + 2 x + y 2 − 4 y =
−1?
A.
B.
C.
D.
E.
6
2
6
4
4
5
4
2
2
-2
-2
-4
-4
2
-5
-2
-6