Answer:
First divide all the equation by three to put in simple form:
x
2
+
y
2
+
4
x
−
2
y
+
3
=
0
Now consider the general equation of the circle is:
(
x
−
x
o
)
2
+
(
y
−
y
o
)
2
−
R
2
=
0
where the center is the point
(
x
o
,
y
o
)
and
R
is the radius.
Expanding:
x
2
−
2
x
x
o
+
x
2
o
+
y
2
−
2
y
y
o
+
y
2
o
−
R
2
=
0
Comparing similar terms, you can easily see that:
−
2
x
o
=
4
⇒
x
o
=
−
2
−
2
y
o
=
−
2
⇒
y
o
=
1
x
2
o
+
y
2
o
−
R
2
=
3
⇒
R
=
√
2
graph{x^2+y^2+4x-2y+3=0 [-10.375, 9.625, -4.08, 5.92]}
