So given the plane: -x-2+2=5 and the line L: (2,1,0) + mu(-1,2,1) how can you find the 2 spheres that are tangent to the plane and whose centres pass through the line and who have radii 4?

help is very appreciated please! thank in advance!

- Nov 1st 2010, 06:06 AMYehiaTo find the equation of a sphere (in 3D space) given a plane, line and radius?
So given the plane: -x-2+2=5 and the line L: (2,1,0) + mu(-1,2,1) how can you find the 2 spheres that are tangent to the plane and whose centres pass through the line and who have radii 4?

help is very appreciated please! thank in advance! - Nov 2nd 2010, 12:49 AMOpalg
The equation of the plane looks odd. I'm guessing that it should actually be .

The centre C of the sphere must lie on the line L, so for some value of . Also, the distance from C to the plane must be 4. The formula for the distance from the point to the plane is . Plug the coordinates of C and the coefficients of the equation of the plane into that formula, set it equal to 4, and you have an equation for the two values of . You then know the coordinates of C, and the rest is easy.