Answer:
Rewrite in standard form to find the center
(
h
,
k
)
and radius
r
.
Center:
(
1
,
−
2
)
Radius:
4
Step-by-step explanation:
Add
11
to both sides of the equation.
x
2
+
y
2
−
2
x
+
4
y
=
11
Complete the square for
x
2
−
2
x
.
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(
x
−
1
)
2
−
1
Substitute
(
x
−
1
)
2
−
1
for
x
2
−
2
x
in the equation
x
2
+
y
2
−
2
x
+
4
y
=
11
.
(
x
−
1
)
2
−
1
+
y
2
+
4
y
=
11
Move
−
1
to the right side of the equation by adding
1
to both sides.
(
x
−
1
)
2
+
y
2
+
4
y
=
11
+
1
Complete the square for
y
2
+
4
y
.
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(
y
+
2
)
2
−
4
Substitute
(
y
+
2
)
2
−
4
for
y
2
+
4
y
in the equation
x
2
+
y
2
−
2
x
+
4
y
=
11
.
(
x
−
1
)
2
+
(
y
+
2
)
2
−
4
=
11
+
1
Move
−
4
to the right side of the equation by adding
4
to both sides.
(
x
−
1
)
2
+
(
y
+
2
)
2
=
11
+
1
+
4
Simplify
11
+
1
+
4
.
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(
x
−
1
)
2
+
(
y
+
2
)
2
=
16
This is the form of a circle. Use this form to determine the center and radius of the circle.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
Match the values in this circle to those of the standard form. The variable
r
represents the radius of the circle,
h
represents the x-offset from the origin, and
k
represents the y-offset from origin.
r
=
4
h
=
1
k
=
−
2
The center of the circle is found at
(
h
,
k
)
.
Center:
(
1
,
−
2
)
These values represent the important values for graphing and analyzing a circle.
Center:
(
1
,
−
2
)
Radius:
4
image of graph
