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3. Using the traces obtained in IV.1., provide a hand-drawn sketch of 3. 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 3.

3. Using the traces obtained in IV.1., provide a hand-drawn sketch of 3. 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 3.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter7: Conic Sections
Section7.3: Hyperbolas
Problem 1E: A hyperbola is the set of all points in the plane for which the ___ of the distances from two fixed...
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IV. Let 3 be the surface with equation given by 4r² - 9y² = 9 (2²+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 3.
Transcribed Image Text:IV. Let 3 be the surface with equation given by 4r² - 9y² = 9 (2²+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 3.
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