# Graphing a Hyperbolic Paraboloid in 3D

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• Published on Mar 26, 2024

In this video I graph a hyperbolic paraboloid, which is a surface that has vertical traces being parabolas, and horizontal traces being hyperbolas. After first obtaining the traces in 2D, I draw them out in 3D, and then combine them all together to form what looks like a horse's saddle. I also graph the hyperbolic paraboloid using the GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec

Time stamps:

• Example 5: Hyperbolic Paraboloid: 0:00
• Solution: Obtaining the traces: 0:10
• Drawing the family of traces: 1:41
• Vertical parabolas in x = k planes: 1:57
• Vertical parabolas in y = k planes: 5:50
• Horizontal hyperbolas in z = k planes: 9:08
• Better graphs from my Calculus book: 16:02
• Fitting traces together to form a Hyperbolic Paraboloid: 17:30
• Better graph from Calculus book: 20:06
• Graphing in GeoGebra: 20:17

Full video below:

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