6. Let S be the surface with equation 4y² + 4z² − x² − 16 = 0 a. Find an equation of the trace of S on each of the coordination planes, and on the planes x = +4√3. Identify each trace. b. Identify the type of quadric surface for S. c. Provide a hand-drawn sketch of S using the traces obtained in (a). label all important points found on each trace. d. Find an equation of a generating curve on the xz-plane if S is viewed as a surface of revolution.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter79: Computing Compound Angles On Cutting And Forming Tools
Section: Chapter Questions
Problem 4A
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6. Let S be the surface with equation 4y² + 4z² − x² - 16 = 0
a. Find an equation of the trace of S on each of the coordination planes, and on the planes x =
+4√3. Identify each trace.
b. Identify the type of quadric surface for S.
c. Provide a hand-drawn sketch of S using the traces obtained in (a). label all important points
found on each trace.
d.
Find an equation of a generating curve on the xz-plane if S is viewed as a surface of
revolution.
Transcribed Image Text:6. Let S be the surface with equation 4y² + 4z² − x² - 16 = 0 a. Find an equation of the trace of S on each of the coordination planes, and on the planes x = +4√3. Identify each trace. b. Identify the type of quadric surface for S. c. Provide a hand-drawn sketch of S using the traces obtained in (a). label all important points found on each trace. d. Find an equation of a generating curve on the xz-plane if S is viewed as a surface of revolution.
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