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Mathematics
Problem
The circles whose equations are
x
2
+
y
2
+
c
2
=
2
a
x
x^2 + y^2 + c^2 = 2ax
x
2
+
y
2
+
c
2
=
2
a
x
and
x
2
+
y
2
+
c
2
−
2
b
y
=
0
x^2 + y^2 + c^2 - 2by = 0
x
2
+
y
2
+
c
2
−
2
b
y
=
0
will touch one another externally, if a.
1
b
2
+
1
c
2
=
1
a
2
\frac{1}{b^2} + \frac{1}{c^2} = \frac{1}{a^2}
b
2
1
+
c
2
1
=
a
2
1
b.
1
c
2
+
1
a
2
=
1
b
2
\frac{1}{c^2} + \frac{1}{a^2} = \frac{1}{b^2}
c
2
1
+
a
2
1
=
b
2
1
c.
1
a
2
+
1
b
2
=
1
c
2
\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2}
a
2
1
+
b
2
1
=
c
2
1
d.
1
b
2
+
1
c
2
=
2
a
2
\frac{1}{b^2} + \frac{1}{c^2} = \frac{2}{a^2}
b
2
1
+
c
2
1
=
a
2
2
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