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Consider S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. Classify what type of quadric is S. 2. Find an equation of the trace of S on the xy-plane, yz-plane, and on the planes y = -1, y = 3, and y = 7. Identify each trace. 3. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 4. Find a generating curve for S (as a surface of revolution) on the yz-plane.

Consider S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. Classify what type of quadric is S. 2. Find an equation of the trace of S on the xy-plane, yz-plane, and on the planes y = -1, y = 3, and y = 7. Identify each trace. 3. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 4. Find a generating curve for S (as a surface of revolution) on the yz-plane.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Analytic Trigonometry
Section2.3: Solving Trigonometric Equations
Problem 11ECP
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Consider S as a quadric with equation 4x² - (y - 3)² + 4z² = 4 1. Classify what type of quadric is S. 2. Find an equation of the trace of S on the xy-plane, yz-plane, and on the planes y = -1, y = 3, and y = 7. Identify each trace. 3. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 4. Find a generating curve for S (as a surface of revolution) on the yz-plane.
Transcribed Image Text:Consider S as a quadric with equation 4x² - (y - 3)² + 4z² = 4 1. Classify what type of quadric is S. 2. Find an equation of the trace of S on the xy-plane, yz-plane, and on the planes y = -1, y = 3, and y = 7. Identify each trace. 3. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 4. Find a generating curve for S (as a surface of revolution) on the yz-plane.
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