FP4 - vectors and matrices

hard to visualise.

Find the Cartesian equation of the plane $\Pi$ that the matrix $\mathbf{M}$
$\begin{bmatrix} 2 & 1 & 0 \\ 0& 1& 0 \\ 4& 2& 0 \end{bmatrix}$
maps all points to under the transformation.
Find the Cartesian equations of the two possible spheres of radii 3 that the plane $\Pi$ is tangent to at the origin.
[The equations should be in exact form not involving trigonometric functions.]

The last bit is aarrrd, hard to visualise.

Okay so for the first part I got the plane $-2x+y=0$, is that right? Been a while since FP4 now I'm trying to remember it.

The last bit is not too bad as far as visualisation goes once you have the plane equation, therefore straight forward to do.

Equation of the plane is $z=2x$.
What about the next part?