Find the equation of the sphere which touches the sphere `x^2+y^2+z^2+2x-6y+1=0` at `(1,2,-2)` and pass through the origin

Write the equation of the sphere concentric with the sphere x^2+y^2+z^2-4x-2x-2y+2z-30=0 and passing through the origin.

Find the equation of the sphere concentric with the sphere x^2+y^2+z^2+4x-6y+8z-5=0 and passing through origin.

The equation of the circle, which touches the parabola y^2=4x at (1,2) and passes through the origin is :

The equation of the circle, which touches the parabola y^2=4x at (1,2) and passes through the origin is :

Equation of the sphere concentric with the sphere x^(2)+y^(2)+z^(2)+2x - 4y + 6z + 12 = 0 and passing through origin is :

Find the equation of the sphere which touches the plane 3x+2y-z+2=0 at the point (1,-2,1) and also cuts the sphere x^(2)+y^(2)+z^(2)-4x+6y+4=0 orthogonally

Find the equation of the circle which touches x^(2) + y^(2) -4x + 6y -1 =0 at (-1,1) internally with a radius of 2.

Find equation of the sphere with centre (3,6,-4) and touching the plane 2x-2y-z-10=0 .

The equations of the sphere concentric with the sphere 2x^(2) +2y^(2) +2z^(2) - 6x +2y -4 z =1 and double its radius is :