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Mathematics
Mathematics
Problem
If the two circles,
x
2
+
y
2
+
2
g
1
x
+
2
f
1
y
=
0
x^2 + y^2 + 2g_1x + 2f_1y = 0
x
2
+
y
2
+
2
g
1
x
+
2
f
1
y
=
0
and
x
2
+
y
2
+
2
g
2
x
+
2
f
2
y
=
0
x^2 + y^2 + 2g_2x + 2f_2y = 0
x
2
+
y
2
+
2
g
2
x
+
2
f
2
y
=
0
touches each other, then (A)
f
1
g
1
=
f
2
g
2
f_1g_1 = f_2g_2
f
1
g
1
=
f
2
g
2
(B)
f
1
g
1
=
f
2
g
2
\frac{f_1}{g_1} = \frac{f_2}{g_2}
g
1
f
1
=
g
2
f
2
(C)
f
1
f
2
=
g
1
g
2
f_1f_2 = g_1g_2
f
1
f
2
=
g
1
g
2
(D) None of these
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