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Mathematics
Mathematics
Problem
A variable plane passes through a fixed point
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
and cuts the coordinate axes at points
A
,
B
A, B
A
,
B
and
C
C
C
. Show that the locus of the centre of the sphere
O
A
B
C
OABC
O
A
B
C
is
a
x
+
b
y
+
c
z
=
2
\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 2
x
a
+
y
b
+
z
c
=
2
.
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