The centre and radius of the given circle is 4x^ 2 + 4y ^ 2 + 36y + 36 = 0
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The centre of the circle is
(
0
,
−
9
2
)
and the radius
=
√
19
Explanation:
We complete the squares
4
x
2
+
4
y
2
+
36
y
+
5
=
0
4
x
2
+
4
(
y
2
+
9
y
)
=
−
5
4
x
2
+
4
(
y
2
+
9
y
+
81
4
)
=
−
5
+
81
4
x
2
+
4
(
y
+
9
2
)
2
=
76
Dividing by
4
x
2
+
(
y
+
9
2
)
2
=
76
4
=
19
So the centre of the circle is
(
0
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