Show that the plane `2x-2y+z+12=0` touches the sphere `x^2+y^2+z^2-2x-4y+2z-3=0.`

The plane 2x-2y+z+12=0 touches the surface x^2+y^2+z^2-2x-4y+2z-3=0 only at point (-1, lambda, -2) . The value of lambda must be

Find the value of lambda for which the plane x+y+z=sqrt(3)lambda touches the sphere x^2+y^2+z^2-2x-2y-2z=6.

The radius of the sphere 3x^2+3y^2+3z^2-8x+4y+8z-15=0 is

A plane P passes through the line of intersection of the planes 2x-y+3z=2,  x+y-z=1 and the point (1,0,1) If the plane P touches the sphere x^2+y^2+z^2=r^2 then what is r equal to?