Sphere

A sphere of constant radius $2k$ passes through the origin and meets the axes in $A,B,C$. The locus of the centroid of the tetrahedron $OABC$ is

The intersection of the spheres $x^2+y^2+z^2+7x-2y-z=13$ and $x^2+y^2+z^2-3x+3y+4z=8$ is same as the intersection of one of the spheres and the plane 

If the plane $2ax-3ay+4az+6=0$ passes through the midpoint of the line joining the centers of the spheres $x^2+y^2+z^2+6x-8y-2z=13$ and $x^2+y^2+z^2-10x+4y-2z=8$, then '$a$' equals

A plane passes through a fixed point $\left(a,b,c\right)$. The locus of the foot of perpendicular to it from the origin is a sphere of radius

The centre of sphere passes through four points $\left(0,0,0\right),\left(0,2,0\right),\left(1,0,0\right)$ and $\left(0,0,4\right)$ is

The equation of the sphere concentric with the sphere $x^2+y^2+z^2-2x-4y+6z+10=0$ and of double its surface area is $x^2+y^2+z^2-2x-4y+6z+k=0$, then $k=$

If plane $2x+3y+6z+k=0$ is tangent to the sphere $x^2+y^2+z^2+2x-2y+2z-6=0$, then the value of $k$ is

The shortest distance from the plane $12x+4y+3z=327$ to the sphere $x^2+y^2+z^2+4x-2y-6z=155$ is

Equation of the sphere with centre $\left(1,-1,1\right)$ and radius equal to that of sphere $2x^2+2y^2+2z^2-2x+4y-6z=1$