Intersection of general plane with quadric surface

[swampwiz]

So far I have calculated this for a cone, which elegantly results in the conic sections. However, I would like to do this for the other quadric surfaces. Is the calculation for this been published anywhere online?

 

[Ssnow]

In general intersecting a plane with a quadratic surface you obtain a quadratic curve. Here a basic .pdf

http://www.win.tue.nl/~sterk/Bouwkunde/hoofdstuk3.pdf

there are no all calculations but in the end some exercises ...