# Calculus 3 Tech Assignment C- Quadrics

Calculus 3 Tech Assignment C- Quadrics using Geogebra Name:____________________________________ Date:_____________________________________ _____/20 All of your work should be compiled in a Microsoft Word document or a PDF and submitted on Blackboard. Name your file with the following naming convention: last name, first name, Tech C Written components should contain articulate thoughts, acceptable grammar, and should be easy to follow. Quadric Surfaces A quadric surface is any 3D surface described by a quadratic equation in three variables: ax 2 + by 2 + cz 2 + dxy + eyz + fxz + gx + hy + jz + k = 0 . Spheres Standard form equation: (x – x0 )2 + ( y – y0 )2 + (z – z 0 )2 = r 2 Use GeoGebra to generate a slider-model for the standard form equation of a sphere. What do each of the constants control? Be specific and use correct vocabulary. (x – x 0 )2 + (y – y0 )2 + (z – z 0 )2 =1 2 2 2 bx by bz Use GeoGebra to generate a slider-model for the standard form equation of an ellipsoid. What do each of the constants control? Be specific and use correct vocabulary. Ellipsoids Standard form equation: Hyperboloids Use GeoGebra to generate a slider-model for each standard form equation below. What do each of the constants control? Be specific and use correct vocabulary. (x – x 0 )2 + (y – y0 )2 – (z – z 0 )2 Elliptic Hyperboloids of One Sheet: bx Elliptic Hyperboloids of Two Sheets: 2 by 2 bz 2 =1 (x – x 0 )2 + (y – y0 )2 – (z – z 0 )2 bx 2 by 2 bz 2 = -1 Paraboloids Use GeoGebra to generate a slider-model for each standard form equation below. What do each of the constants control? Be specific and use correct vocabulary. Elliptic Paraboloids: z – z 0 = (x – x 0 )2 + (y – y0 )2 Hyperbolic Paraboloids: z – z 0 bx 2 by 2 2 2 ( x – x 0 ) (y – y 0 ) = – bx 2 by 2 ..18 T-Mobile 10:44 AM 12% Done 20210407124546tech_assignme… Paraboloids Use GeoGebra to generate a slider-model for each standard form equation below. What do each of the constants control? Be specific and use correct vocabulary. Elliptic Paraboloids: z-Z, = (x – x.)? (y- y.)? b, b, + 2 2 X y Hyperbolic Paraboloids: z-z (x – x,)(y-y.) b.2 by ly 2 X 6
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