Home
Class 12
MATHS
A sphere of constant radius k , passe...

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

Promotional Banner

Similar Questions

Explore conceptually related problems

If a circle of constant radius 3k passes through the origin and meets the axes in A and B, then the locus of the centroid of triangleOAB is :

If the plane 7x+11y+13z=3003 meets the axes A, B, C then the centroid of the triangle ABC is

A variable plane is at a constant distance k from the origin and meets the coordinate axes at A, B, C. Then the locus of the centroid of the triangle ABC is

If the plane 3x+4y-3z+2=0 cuts the coordinate axes at A, B, C, then the centroid of the triangle ABC is

If a plane meets coordinate axes in A, B, C such that the centroid of the triangle is (1, k, k^2) , then equation of the plane is :

The plane x/2+y/3+z/4 = 1 cuts the axes A, B, C then the area of the triangle ABC is

Find the centre and radius of the sphere 2x^2+2y^2+2z^2-2x-4y+2z+3=0 .

The centroid of the triangle A B C is (2,3) and A=(4,2), B=(4,5), then the area of the triangle A B C

The circle, which passes through the origin and whose centre lies on the line y = x and cutting the circle x^2+y^2-4x-6y+10 = 0 orthogonally is :

If a circle passes through the point (a, b) circle x^2 + y^2 - k^2 = 0 orthogonally, then the equation of the locus of its centre is :