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Mathematics
Mathematics
Problem
A variable plane which remains at a constant distance
p
p
p
from the origin cuts the coordinate axes in
A
,
B
,
C
A, B, C
A
,
B
,
C
. The locus of the centroid of the tetrahedron
O
A
B
C
OABC
O
A
B
C
is
x
2
y
2
+
y
2
z
2
+
z
2
x
2
=
k
p
2
x
2
y
2
z
2
x^2 y^2 + y^2 z^2 + z^2 x^2 = \frac{k}{p^2} x^2 y^2 z^2
x
2
y
2
+
y
2
z
2
+
z
2
x
2
=
p
2
k
x
2
y
2
z
2
, then
2
k
3
\sqrt[3]{2k}
3
2
k
is
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