Given are the line l (10/0/0)+m*(-6/5/11), the Plane P:x-8=0 and the plane E z=0

sought is the Center C (which lies on l) of the sphere S which touches both E and P.

My idea: the center C is given as (10-6m)/5m/11m. The distance from C to E and E must be the same, so we can use the "hessian normal form" in order to find a point that hast the same d to E and P.

(10-6m)-8=11m. M=2/17

unfortunately this is wrong. Anyone a idea why?