The equation $ax^2 + by^2 + cz^2 + 2fyz + 2gxz + 2hxy + 2ux + 2vy + 2wz + d = 0$ represents a sphere,if:

If $r$ is the position vector of any point on a sphere and $a$ and $b$ are the position vectors of the extremities of a diameter,then which of the following is true?

The ratio in which the sphere ${x^2} + {y^2} + {z^2} = 504$ divides the line segment $AB$ joining the points $A(12, -4, 8)$ and $B(27, -9, 18)$ is given by

The equation of the sphere passing through the points $(1,0,0), (0,1,0)$ and $(1,1,1)$ and having the smallest radius 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 the same as the intersection of one of the spheres and the plane:

$A$ spherical ball is kept at the corner of a rectangular room such that the ball touches two perpendicular walls and lies on the floor. If a point on the sphere is at distances of $9, 16, 25$ from the two walls and the floor,then a possible radius of the sphere is