A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the center of the sphere OABC, O being the origin, is

\(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} + \frac{{\rm{z}}}{{\rm{c}}} = 2\)

\(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} + \frac{{\rm{z}}}{{\rm{c}}} = 1\)

\(\frac{{\rm{a}}}{{\rm{x}}} + \frac{{\rm{b}}}{{\rm{y}}} + \frac{{\rm{c}}}{{\rm{z}}} = 1\)

\(\frac{{\rm{a}}}{{\rm{x}}} + \frac{{\rm{b}}}{{\rm{y}}} + \frac{{\rm{c}}}{{\rm{z}}} = 2\)

A variable plane passes through a fixed point (a, b, c) and cuts the a

1.	A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the center of the sphere OABC, O being the origin, is
A.	\(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} + \frac{{\rm{z}}}{{\rm{c}}} = 1\)
B.	\(\frac{{\rm{a}}}{{\rm{x}}} + \frac{{\rm{b}}}{{\rm{y}}} + \frac{{\rm{c}}}{{\rm{z}}} = 1\)
C.	\(\frac{{\rm{a}}}{{\rm{x}}} + \frac{{\rm{b}}}{{\rm{y}}} + \frac{{\rm{c}}}{{\rm{z}}} = 2\)
D.	\(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} + \frac{{\rm{z}}}{{\rm{c}}} = 2\)
Answer» D. \(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} + \frac{{\rm{z}}}{{\rm{c}}} = 2\)

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A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the center of the sphere OABC, O being the origin, is

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