Using the traces obtained in IV.1., provide a hand-drawn sketch of S3. Label all important points (e.g., vertices) found on each trace. (For graphing purposes, 3√/2≈ 4.2.) View S3 as a surface of revolution. Find an equation of a generating curve on the xy-plane which, if revolved about the x-axis, will result to 3.
Using the traces obtained in IV.1., provide a hand-drawn sketch of S3. Label all important points (e.g., vertices) found on each trace. (For graphing purposes, 3√/2≈ 4.2.) View S3 as a surface of revolution. Find an equation of a generating curve on the xy-plane which, if revolved about the x-axis, will result to 3.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 35E
Related questions
Question
Please answer 3 and 4.
![Let 3 be the surface with equation given by 4x² − 9y² = 9 (z² + 4).
1. Find an equation of the trace of S3 on each of the coordinate planes and on the planes x = ±3√2.
Determine if each trace is empty, a point, a (pair of) line(s), a parabola, an ellipse, or a hyperbola.
2. What type of quadric surface is S3?
3. Using the traces obtained in IV.1., provide a hand-drawn sketch of S3. Label all important points
(e.g., vertices) found on each trace. (For graphing purposes, 3√2≈ 4.2.)
4. View 3 as a surface of revolution. Find an equation of a generating curve on the xy-plane which,
if revolved about the x-axis, will result to I 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabb17ac1-b0e7-4613-84db-09be781cd09d%2Fb14c2a79-5e46-44b6-bb3a-a75d7089acdd%2F9vb1rbk_processed.png&w=3840&q=75)
Transcribed Image Text:Let 3 be the surface with equation given by 4x² − 9y² = 9 (z² + 4).
1. Find an equation of the trace of S3 on each of the coordinate planes and on the planes x = ±3√2.
Determine if each trace is empty, a point, a (pair of) line(s), a parabola, an ellipse, or a hyperbola.
2. What type of quadric surface is S3?
3. Using the traces obtained in IV.1., provide a hand-drawn sketch of S3. Label all important points
(e.g., vertices) found on each trace. (For graphing purposes, 3√2≈ 4.2.)
4. View 3 as a surface of revolution. Find an equation of a generating curve on the xy-plane which,
if revolved about the x-axis, will result to I 3.
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