Drawing a hyperboloid of one sheet – emphasis on vertical sections

When you view a hyperboloid of one sheet from the side, you can see a hyperbola. Horizontal cross sections are ellipses and sections in vertical planes are hyperbolas in different directions or just two lines.
1. Draw a hyperbola opening sideways – remember hyperbolas are almost straight at the edge and turn quite sharply in the middle.
2. Draw an ellipse at the top, and an ellipse arc at the bottom.
3. Fill in horizontal sections – it works well to start in the middle.
4. Draw two lines crossing on the centre horizontal section.
5. Draw upper and lower branches of a hyperbola inside the two lines.
6. Draw left and right branches of a hyperbola outside the two lines.


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