Then all points are negative. Consider the point p=(0,0,0)∈S, whose tangent plane is the plane z=0. Let c>0. Then the intersection of S with planes parallel to TpS is S∩{z=c}={(x,y,c):x2−y2=c}={(x,y,c):(x√c)2−(y√c)2=1},
that is, an ellipse, for each height c>0. Similarly, for c<0.
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