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 $\displaystyle -x-2y+2z = 5$.

The centre C of the sphere must lie on the line L, so $\displaystyle C = (2-\mu,1+2\mu,\mu)$ for some value of $\displaystyle \mu$. Also, the distance from C to the plane must be 4. The formula for the distance from the point $\displaystyle (x_0,y_0,z_0)$ to the plane $\displaystyle ax+by+cz=d$ is $\displaystyle \frac{|ax_0+by_0+cz_0-d|}{\sqrt{a^2+b^2+c^2}}$. 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 $\displaystyle \mu$. You then know the coordinates of C, and the rest is easy.