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प्रश्न
A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is `1/x^2 + 1/y^2 + 1/z^2 = 1/p^2`
उत्तर
Let the equation of the plane be
From (ii), we have
a = 3α ,b = 3β and c = 3γ
Substituting the values of a, b, c in (iii), we obtain
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