(a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b) If we change the equation in part (a) to x2 -y2 +z2 =1 , how is the graph affected? (c) What if we change the equation in part (a) to x2 +y2 +2y- z2 =0?
(a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b) If we change the equation in part (a) to x2 -y2 +z2 =1 , how is the graph affected? (c) What if we change the equation in part (a) to x2 +y2 +2y- z2 =0?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 40E
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(a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1.
(b) If we change the equation in part (a) to x2 -y2 +z2 =1 , how is the graph affected?
(c) What if we change the equation in part (a) to x2 +y2 +2y- z2 =0?
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