A variable plane `x/a+y/b+z/c=1` at a unit distance from origin cuts the coordinate axes at `A, B and C.` Centroid `(x, y, z)` satisfies the equation `1/x^2+1/y^2+1/z^2=K.` The value of `K` is (A) `9` (B) `3` (C) `1/9` (D) `1/3`

A variable plane which is at a constant distance 3p from origin cuts the coordinate axes at A,B,C respectively. Show that locus of the centroid of the triangleABC is 1/x^2+1/y^2+1/z^2= 1/p^2 .

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B and C , show that the locus of the centroid of the tetrahedron OABC os 1/x^2+1/y^2+1/z^2= 16/p^2

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B and C. Show that the locus of the centroid of the tetrahedron OABC is (1)/(x^2)+(1)/(y^2)+(1)/(z^2)=(16)/(p^2) .

a variable plane which is at a constant distance 3p from the origin O cuts the axes at A,B,C. Show that the locus of the centroid of the triangle ABC is x^(-2)+y^(-2)+z^(-2)=p^(-2) .

A sphere of constant radius k passes through the origin and meets the axes at A, B and C. Prove that the centroid of triangle ABC lies on the sphere 9(x^(2)+y^(2)+z^(2))=4k^(2) .

If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a circle, when m is (a) 1/2 (b). 1 (c). 2 (d). 3

If a, b, c and x, y, z are positive, then show that (a/x + b/y + c/z) (x/a + y/b + z/c) ge 9

If x+y=k is normal to y^2=12 x , then k is (a)3 (b) 9 (c) -9 (d) -3

If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x , y , z) that satisfy the equation is 0 (b) 1 (c) 2 (d) Infinite solutions

If the prependicular distance of a plane from the origin is 1 and direction cosines of normal vector of the plane satisfies (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=K where (x,y,z ) is the centroid of the triangle make by intercept point of axis then K equals__