6. Consider the surface in R³ defined by x² + y² - 2z² + 6x - 8z = 7. (a) This surface is a quadric surface. Identify the surface by name. Briefly justify your answer. (b) Show that the point P(2, 1, 1) is on the surface.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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6. Consider the surface in R³ defined by
x² + y² -
22² + 6x - 8z = 7.
(a) This surface is a quadric surface. Identify the surface by name. Briefly justify your
answer.
(b) Show that the point P(2, 1, 1) is on the surface.
Transcribed Image Text:6. Consider the surface in R³ defined by x² + y² - 22² + 6x - 8z = 7. (a) This surface is a quadric surface. Identify the surface by name. Briefly justify your answer. (b) Show that the point P(2, 1, 1) is on the surface.
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