Consider 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.

Consider 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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.1: Parabolas

Problem 34E

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