Thread: 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?

Originally Posted by Schdero

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.