Find the centre and radius of the circle x² + y²-12x + 6y +45-0
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x
2
+
y
2
+
12
x
−
6
y
=
0
First we can collect "like" terms:
{
x
2
+
12
x
}
+
{
y
2
−
6
}
=
0
Next we complete the square independently on the
x
and
y
terms
∴
{
(
x
+
6
)
2
−
6
2
}
+
{
(
y
−
3
)
2
−
3
2
}
=
0
∴
(
x
+
6
)
2
−
36
+
(
y
−
3
)
2
−
9
=
0
∴
(
x
+
6
)
2
+
(
y
−
3
)
2
=
36
+
9
∴
(
x
+
6
)
2
+
(
y
−
3
)
2
=
45
∴
(
x
+
6
)
2
+
(
y
−
3
)
2
=
(
3
√
5
)
2
And as such, we can identify the conic as an circle with radius
3
√
5
, and centre
(
−
6
,
3
)
graph{x^2 + y^2 + 12x - 6y = 0 [-24.5, 15.5, -6.32, 13.68]}
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