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Intro to Quadric Surfaces and Recap on Conic Sections

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First published at 20:18 UTC on March 20th, 2024.

#math
#geometry
#science

Math Easy Solutions

MES

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In this video i go over a quick introduction to 3D Quadric Surfaces and recap on their 2D counterparts, Conic Sections. A quadric surface is the 3D graph of a second-degree equation in three variables x, y, and z. I illustrate the most general equation as well as two standard forms that be obtained by rotation and translation (and lots of algebra via completing the square). Quadric surfaces have 2D counterparts in conic sections, which I have listed below.

Ellipsoid vs Ellipse
Paraboloid vs parabola
Hyperboloid vs hyperbola

I also go over a recap on the equations and graphs of conic sections.

GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec

Time stamps:

- Quadric Surfaces have second-degree equations: 0:00
- General equation: 0:15
- Two Standard Form equations: 1:33
- Recap on conic sections: 3:08

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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