Suppose is the surface generated by revolving the curve y = 4(x² - 1) about the y-axis. 1. Determine an equation of S. What type of quadric surface is S? 2. Write the equation of the trace of on each coordinate plane and identify the type of conic each equation represents. 3. Provide a hand-drawn sketch of using the traces obtained in 2. Label important points.

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 38E
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Suppose is the surface generated by revolving the curve y = 4(x² − 1) about the y-axis.
1. Determine an equation of S. What type of quadric surface is S?
2. Write the equation of the trace of on each coordinate plane and identify the type of conic each
equation represents.
3. Provide a hand-drawn sketch of
using the traces obtained in 2. Label important points.
Transcribed Image Text:Suppose is the surface generated by revolving the curve y = 4(x² − 1) about the y-axis. 1. Determine an equation of S. What type of quadric surface is S? 2. Write the equation of the trace of on each coordinate plane and identify the type of conic each equation represents. 3. Provide a hand-drawn sketch of using the traces obtained in 2. Label important points.
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