Answer:
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Algebra Examples
Popular Problems Algebra Find the Center and Radius x^2+y^2-8y=0
x
2
+
y
2
−
8
y
=
0
Complete the square for
y
2
−
8
y
.
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(
y
−
4
)
2
−
16
Substitute
(
y
−
4
)
2
−
16
for
y
2
−
8
y
in the equation
x
2
+
y
2
−
8
y
=
0
.
x
2
+
(
y
−
4
)
2
−
16
=
0
Move
−
16
to the right side of the equation by adding
16
to both sides.
x
2
+
(
y
−
4
)
2
=
0
+
16
Add
0
and
16
.
x
2
+
(
y
−
4
)
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
=
0
k
=
4
The center of the circle is found at
(
h
,
k
)
.
Center:
(
0
,
4
)
These values represent the important values for graphing and analyzing a circle.
Center:
(
0
,
4
)
Radius:
4
