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Math Help - Sphere touching two planes

  1. #1
    Junior Member
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    Sphere touching two planes

    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?
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Schdero View Post
    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?
    Here are few comments:

    When you formed the equation:
    (10-6m)-8=11m
    you assumed the direction of normal for plane P as "+x" and direcion of normal for plane E as "+z". Now, the these two planes divide the space in four parts. These four parts are:
    (1)Points lying above E and right of P
    (2)Points lying above E and left of P
    (3)Points lying below E and right of P
    (4)Points lying below E and left of P
    (Imagine a horizontal x-axis and vertical z-axis to understand the above four cases)

    Now, you equation covers only the parts (1) and (4) (why?????)

    When you consider the parts (2) and (3), you get m=-2/5.

    If you can't work out yet, ask for details.
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