The plane `x+2y-z=4` cuts the sphere `x^(2)+y^(2)+z^(2)-x+z-2=0` in a circle of radius

The length of the radius of the sphere x^(2)+y^(2)+z^(2)+2x-4y=10 is

If plane 2x+3y+6z+k=0 is tangent to the sphere x^(2)+y^(2)+z^(2)+2x-2y+2z-6=0 , then a value of k is (a) 26 (b) 16 (c) -26 (d) none of these

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

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

The lines x=y=z meets the plane x+y+z=1 at the point P and the sphere x^2+y^2+z^2=1 at the point R and S, then

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

The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4z-19=0 is cut by the plane x+2y+2z+7=0 is a. 2 b. 3 c. 4 d. 1

Find the equation the equation of sphere cocentric with sphere 2x^2+2y^2+2z^2-6x+2y-4z=1 and double its radius.

The line (x)/(1) = y/2=z/3 and the plane x-2y+ z=0:

Factorise 4x^2+y^2+z^2-4x y-2y z+4x z .