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Mathematics
Mathematics
Problem
If the equation of the locus of point equidistant from the points
(
a
1
,
b
1
)
(a_1, b_1)
(
a
1
,
b
1
)
and
(
a
2
,
b
2
)
(a_2, b_2)
(
a
2
,
b
2
)
is
(
a
1
−
a
2
)
x
+
(
b
1
−
b
2
)
y
+
c
=
0
(a_1 - a_2)x + (b_1 - b_2)y + c = 0
(
a
1
−
a
2
)
x
+
(
b
1
−
b
2
)
y
+
c
=
0
, then
c
=
c =
c
=
(a)
a
1
2
−
a
2
2
+
b
1
2
−
b
2
2
a_1^2 - a_2^2 + b_1^2 - b_2^2
a
1
2
−
a
2
2
+
b
1
2
−
b
2
2
(b)
1
2
(
a
1
2
+
a
2
2
+
b
1
2
+
b
2
2
)
\frac{1}{2}(a_1^2 + a_2^2 + b_1^2 + b_2^2)
2
1
(
a
1
2
+
a
2
2
+
b
1
2
+
b
2
2
)
(c)
(
a
1
2
+
b
1
2
−
a
2
2
−
b
2
2
)
\sqrt{(a_1^2 + b_1^2 - a_2^2 - b_2^2)}
(
a
1
2
+
b
1
2
−
a
2
2
−
b
2
2
)
(d)
1
2
(
a
2
2
+
b
2
2
−
a
1
2
−
b
1
2
)
\frac{1}{2}(a_2^2 + b_2^2 - a_1^2 - b_1^2)
2
1
(
a
2
2
+
b
2
2
−
a
1
2
−
b
1
2
)
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