Graphing a Hyperboloid of Two Sheets in 3D
In this video I sketch a hyperboloid of two sheets, which is a quadric surface with horizontal traces being hyperbolas while vertical traces are comprised of both hyperbolas and ellipses. There are no vertical traces in the xz-plane thus the quadric surface is split into two sheets, hence the name: Hyperboloid of Two Sheets.
GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec
Time stamps:
- Example 7: Hyperboloid of Two Sheets: 0:00
- Solution: Re-arranging equation into standard form: 0:17
- Comparing equation with hyperboloid of two sheets from Table 1: 1:56
- Traces in xy and yz-planes are hyperbolas: 2:09
- Traces in y = k planes are ellipses: 3:41
- No traces in the xz-plane: 5:57
- Re-writing y = k traces equation: 6:44
- Sketching the graph using traces: 7:48
- Graphing in GeoGebra: 10:55
Full video below:
- Cylinders and Quadric Surfaces:
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- Cylinders and Quadric Surfaces: