# Math Help - Planes, sphere

1. ## Planes, sphere

Given is 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?

2. Originally Posted by Schdero
Given is 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?
I think your basic idea is right. But there are two solutions that you get from $|(10-6m)-8|=|11m|$, one solution is your $m_1=2/17$ which gives $C_1=(\frac{158}{17}/\frac{10}{17}/\frac{22}{17})$, and the other solution is $m_2=-2/5$ which gives $C_2=(\frac{62}{5}/-2/-\frac{22}{5})$.
I don't think that your solution is wrong, it is just not the only solution.