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Math Help - Planes, sphere

  1. #1
    Junior Member
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    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?
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by Schdero View Post
    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.
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