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This Demonstration shows the intersections of planes perpendicular to the axes with plots of quadratic forms, which are paraboloids, hyperbolic paraboloids, ellipsoids, cones, or hyperboloids of one or two sheets.

The graph of the equation ax^2 + by^2 + cz^2 + dxy + exz + fyz +gx + hj + i z + j=0 is shown for your settings of the parameters.

Set d=e=f=0 to keep things centered at the origin. To get the paraboloids you want one of (g,h,i) to be nonzero. To get the hyperboloids set g=h=i=0 and let a, b, c be mixed signs. To get the ellipsoids make sure a, b, and c are all negative. See if you can find a setting where a single parameter changes the surface from a hyperboloid of two sheets, to a cone, to a hyperboloid of one sheet.