[Maxima] Eliminating parameters for computing an intersection

[Richard Fateman]

Reinhard Jansohn wrote:
> Hello Maxima friends!
>
> I computed the intersection of two cylinders by hand as shown below but I want to compute similar intesections with Maxima. 
>
> Please note that there is an article "The Geometry of Intersecting Tubes Applied to Controlling a Robotic Welding Torch" from by John M. Stockie on the web http://www.math.sfu.ca/~stockie/weld/ showing how this is done in Maple. Unfortunately I could not do that in Maxima.
>   

Why don't you list the Maple commands to do the part of the task you are 
interested in,
and then show how where you could not get with Maxima.
It seems to me that all you need is subst and solve, and some tricks
where you introduce z and simplify.