What is the x intercepts of the mid point f(x)=(x-2)(x-4)
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The cylinder is a clue to use cylindrical coordinates. Taking 
and 
, we then are forced to use 
. So the parameterization of the intersection of the plane and cylinder is
To get the surface, we can introduce a second parameter
that "contracts" the elliptical intersection to a point. The simplest way to do this is to use
with
and 
.
To get the surface, we can introduce a second parameter
with