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: https://youtu.be/k4EyLr4uOUA
- HIVE video notes: https://peakd.com/hive-128780/@mes/cylinders-and-quadric-surfaces
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EfmYwT81SebJnU1Ny8Fc5u
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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