[math-fun] sections of quadratic surfaces

Some find it counterintuitive that slicing a cone gives an ellipse and not an oval. What about slicing a paraboloid of rotation? More generally how can eliminating a quadratic mumbloid vs a linear (planar) equation yield anything but a quadratic (conic)? --rwg o o o o o o o o o o o o o o o o o o o o o o o o o kosher kosher salt