(4) Consider the following set: S = {(x, y, z) E R | xy + yz + x = -2}. (a) Show that S is a surface. (b) Give a parametrisation of S such that (-1, 1, 0) lies in the image of S. (c) Compute the tangent plane to S at (-1, 1,0).
(4) Consider the following set: S = {(x, y, z) E R | xy + yz + x = -2}. (a) Show that S is a surface. (b) Give a parametrisation of S such that (-1, 1, 0) lies in the image of S. (c) Compute the tangent plane to S at (-1, 1,0).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Question
![(4)
Consider the following set:
S = {(x, y, z) E R' | xy + yz + x =-2}.
(a) Show that S is a surface.
(b) Give a parametrisation of S such that (-1,1,0) lies in the image of S.
(c) Compute the tangent plane to S at (-1, 1, 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F237060cb-7ece-4dbe-bd15-cc77668a891c%2F73b8a71e-8084-4f90-a0c8-c677692a7b0c%2F3vjfoh5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(4)
Consider the following set:
S = {(x, y, z) E R' | xy + yz + x =-2}.
(a) Show that S is a surface.
(b) Give a parametrisation of S such that (-1,1,0) lies in the image of S.
(c) Compute the tangent plane to S at (-1, 1, 0).
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