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Given S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. 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. 2. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 3. Find a generating curve for S (as a surface of revolution) on the yz-plane.

Given S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. 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. 2. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 3. Find a generating curve for S (as a surface of revolution) on the yz-plane.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. 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. 2. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 3. Find a generating curve for S (as a surface of revolution) on the yz-plane.
Transcribed Image Text:Given S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. 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. 2. Using the traces obtained, draw a sketch of graph of S, with complete label of important points. (For graph: √5 ≈ 2.2) 3. Find a generating curve for S (as a surface of revolution) on the yz-plane.
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