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Mathematics
Problem
If a circle passes through the point
(
a
,
b
)
(a, b)
(
a
,
b
)
and cuts the circle
x
2
+
y
2
=
4
x^2 + y^2 = 4
x
2
+
y
2
=
4
orthogonally, then the locus of its centre is a.
2
a
x
+
2
b
y
+
(
a
2
+
b
2
+
4
)
=
0
2ax + 2by + (a^2 + b^2 + 4) = 0
2
a
x
+
2
b
y
+
(
a
2
+
b
2
+
4
)
=
0
b.
2
a
x
+
2
b
y
−
(
a
2
+
b
2
+
4
)
=
0
2ax + 2by - (a^2 + b^2 + 4) = 0
2
a
x
+
2
b
y
−
(
a
2
+
b
2
+
4
)
=
0
c.
2
a
x
−
2
b
y
+
(
a
2
+
b
2
+
4
)
=
0
2ax - 2by + (a^2 + b^2 + 4) = 0
2
a
x
−
2
b
y
+
(
a
2
+
b
2
+
4
)
=
0
d.
2
a
x
−
2
b
y
−
(
a
2
+
b
2
+
4
)
=
0
2ax - 2by - (a^2 + b^2 + 4) = 0
2
a
x
−
2
b
y
−
(
a
2
+
b
2
+
4
)
=
0
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