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Step-by-step explanation:
Use the standard form to write two equations using points A and B:
(
−
2
−
h
)
2
+
(
0
−
k
)
2
=
r
2
(
5
−
h
)
2
+
(
1
−
k
)
2
=
r
2
Because
r
2
=
r
2
, we can set the left sides equal:
(
−
2
−
h
)
2
+
(
0
−
k
)
2
=
(
5
−
h
)
2
+
(
1
−
k
)
2
Expand the squares using the pattern
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
4
+
4
h
+
h
2
+
k
2
=
25
−
10
h
+
h
2
+
1
−
2
k
+
k
2
Combine like terms (noting that the squares cancel):
4
+
4
h
=
25
−
10
h
+
1
−
2
k
Move the k term the left and all other terms to the right:
2
k
=
−
14
h
+
22
Divide by 2
k
=
−
7
h
+
11
[1]
Evaluate the given line at the center point:
2
h
+
k
−
1
=
0
Write in slope-intercept form
k
=
−
2
h
+
1
[2]
Subtract equation [2] from equation [1]:
k
−
k
=
−
7
h
+
2
h
+
11
−
1
0
=
−
5
h
+
10
h
=
2
Substitute 2 for h in equation [2]
k
=
−
2
(
2
)
+
1
k
=
−
3
Substitute the center
(
2
,
−
3
)
into the equation of a circle using point A and solve for the value of r:
(
−
2
−
2
)
2
+
(
0
−
−
3
)
2
=
r
2
(
−
4
)
2
+
3
2
=
r
2
r
2
=
25
r
=
5
Substitute the center
(
2
,
−
3
)
and #r = 5 into the general equation of a circle, to obtain the specific equation for this circle:
(
x
−
2
)
2
+
(
y
−
−
3
)
2
=
5
2