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.
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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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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