1. The problem statement, all variables and given/known data I was sitting drinking a cup of tea earlier. The cup was of course cylindrical. I was just gazing into the cup looking at the tea as my cup was flat and the top level of the tea looked like a circle. Watching the tea as I tilted the cup to drink I noticed that the shape of the top level of tea changed in the way a circle might if you stretched it. Is it the case that the shape of the tea moves from a circle, when my cup is upright, through a parabola and then an ellipse? I am sorry I do not know anything about conic sections other than that you can get them by slicing through cones at various angles. Having looked them up online, I can't tell without some equations representing the shape made by my tea, if the curves are either of these conic sections. I don't know enough to say just by looking and I don't know if the parabola or the ellipse comes first i.e. with a slight tilt of the cup. Obviously a very full cup cannot tilt much without spillage so let's assume any old cylindrical cup that is half full. Thanks in advance.