Which surface is created by the intersection of the cylinder and the plane

That is, the cylinder cuts out a surface from the plane.

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- Sep 18th 2008, 11:44 AMSpec[SOLVED] Surface
Which surface is created by the intersection of the cylinder and the plane

That is, the cylinder cuts out a surface from the plane. - Sep 18th 2008, 01:54 PMLaurent
Drawing a sketch is very helpful (in this case, it is not very difficult to do).

First we choose a coordinate system in the plane , i.e. an origin and an orthonormal basis , so we can write the equation of the intersection using it. For instance (as shows the sketch, it is not only a simple but also an appropriate choice), , and .

Then, for any in the intersection, , hence , so the coordinates of in the new system are and . The equation becomes . In other words, the intersection is an ellipse with minor and major axes respectively equal to and , centered at . The major axis is in direction and the minor one in direction . - Sep 18th 2008, 02:42 PMshawsend
That's very nice Laurent. I used your equation in the form of:

;

Then did a parametric plot of (in red) over the range

and then plotted it with the cylinder and plane so defined: