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1. Let A be the surface with the equation given by 4x² - 9y² = 9 (z²+4). a. Find an equation of the trace of A 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. b. What type of quadric surface is A? c. Using the traces obtained in 1a, provide a hand-drawn sketch of A. Label all important points (e.g., vertices) found on each trace. (For graphing purposes, 3√2≈ 4.2.)

1. Let A be the surface with the equation given by 4x² - 9y² = 9 (z²+4). a. Find an equation of the trace of A 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. b. What type of quadric surface is A? c. Using the traces obtained in 1a, provide a hand-drawn sketch of A. Label all important points (e.g., vertices) found on each trace. (For graphing purposes, 3√2≈ 4.2.)

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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1. Let A be the surface with the equation given by 4x² - 9y² = 9 (z²+ 4). a. Find an equation of the trace of A 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. b. What type of quadric surface is A? c. Using the traces obtained in 1a, provide a hand-drawn sketch of A. Label all important points (e.g., vertices) found on each trace. (For graphing purposes, 3√2~4.2.) d. View A 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 in A.
Transcribed Image Text:1. Let A be the surface with the equation given by 4x² - 9y² = 9 (z²+ 4). a. Find an equation of the trace of A 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. b. What type of quadric surface is A? c. Using the traces obtained in 1a, provide a hand-drawn sketch of A. Label all important points (e.g., vertices) found on each trace. (For graphing purposes, 3√2~4.2.) d. View A 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 in A.
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