Answer:
(
x
−
5
3
)
2
+
(
y
−
5
3
)
2
−
65
9
=
0
Explanation:
The circle's general equation is
C
→
(
x
−
x
0
)
2
+
(
y
−
y
0
)
2
−
r
2
=
0
This equation must be obeyed by the three points. Substituting
{
x
,
y
}
for each point we have
⎧
⎪
⎪
⎨
⎪
⎪
⎩
2
x
0
+
x
2
0
−
4
y
0
+
y
2
0
+
5
−
r
2
=
0
−
6
x
0
+
x
2
0
−
8
y
0
+
y
2
0
+
25
−
r
2
=
0
−
4
x
0
+
x
2
0
+
2
y
0
+
y
2
0
+
5
−
r
2
=
0
Those equations are easily handled taking the difference between the first and the second, and the first and the third, obtaining
{
2
x
0
+
y
0
−
5
=
0
x
0
−
y
0
=
0
Solving for
x
0
,
y
0
we obtain
{
x
0
=
5
3
,
y
0
=
5
3
}
r
is obtained putting those results in any of the equations already obtained
r
=
√
65
3
Step-by-step explanation:
