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III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? 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. b. Provide a hand-drawn sketch of S using the traces obtained in (a). Label all important points found on each trace (Note: For graphing purposes √√5 ≈ 2.2). c. The quadric S can also be identified as a surface of revolution. Find a generating curve for S on the yz-plane.

III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? 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. b. Provide a hand-drawn sketch of S using the traces obtained in (a). Label all important points found on each trace (Note: For graphing purposes √√5 ≈ 2.2). c. The quadric S can also be identified as a surface of revolution. Find a generating curve for S on the yz-plane.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? 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. b. Provide a hand-drawn sketch of S using the traces obtained in (a). Label all important points found on each trace (Note: For graphing purposes √√5 ≈ 2.2). c. The quadric S can also be identified as a surface of revolution. Find a generating curve for S on the yz-plane.
Transcribed Image Text:III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? 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. b. Provide a hand-drawn sketch of S using the traces obtained in (a). Label all important points found on each trace (Note: For graphing purposes √√5 ≈ 2.2). c. The quadric S can also be identified as a surface of revolution. Find a generating curve for S on the yz-plane.
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