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Mathematics
Problem
Consider a circle
C
1
:
x
2
+
y
2
−
4
x
−
2
y
=
α
−
5
C_1: x^2 + y^2 - 4x - 2y = \alpha - 5
C
1
:
x
2
+
y
2
−
4
x
−
2
y
=
α
−
5
. Let its mirror image in the line
y
=
2
x
+
1
y = 2x + 1
y
=
2
x
+
1
be another circle
C
2
:
5
x
2
+
5
y
2
−
10
f
x
−
10
g
y
+
36
=
0
C_2: 5x^2 + 5y^2 - 10fx - 10gy + 36 = 0
C
2
:
5
x
2
+
5
y
2
−
10
f
x
−
10
g
y
+
36
=
0
. Let
r
r
r
be the radius of
C
2
C_2
C
2
. Then,
α
+
r
\alpha + r
α
+
r
is equal to ...... (2023 Main, 8 April I)
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