By expanding
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
, we obtain
x
2
−
2
h
x
+
h
2
−
2
k
y
+
k
2
−
r
2
=
0
. When we compare this result to the form
x
2
+
y
2
+
D
x
+
E
y
+
F
=
0
, we see that
D
=
−
2
h
,
E
=
−
2
k
, and
F
=
h
2
+
k
2
−
r
2
. Therefore, the center and the length of a radius of a circle can be found by using
h
=
D
−
2
,
k
=
E
−
2
and
r
=
h
2
+
k
2
−
F
. Use these relationship to find the center and the length of the radius of each of the following circles.
x
2
+
y
2
+
4
x
−
14
y
+
49
=
0