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(a)i- Show that the following equation represents a sphere, and find its center and radius. x² + y² + z² + (-10) x + (−2) y + (−8) z + 38 = (b) Find an equation of the sphere that passes through the point (-2, 0, 1) and centered at the point (0, 1, 1). (c)! Does the point P(3, 1, 0) belong to the sphere found in part (b)? Justify your answer.

(a)i- Show that the following equation represents a sphere, and find its center and radius. x² + y² + z² + (-10) x + (−2) y + (−8) z + 38 = (b) Find an equation of the sphere that passes through the point (-2, 0, 1) and centered at the point (0, 1, 1). (c)! Does the point P(3, 1, 0) belong to the sphere found in part (b)? Justify your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Work Problem 1. J (a)i- Show that the following equation represents a sphere, and find its center and radius. x² + y² + z² + (-10) x + (−2) y + (−8) z + 38 = 0 (b) Find an equation of the sphere that passes through the point (-2, 0, 1) and centered at the point (0, 1, 1). (c)! Does the point P(3, 1, 0) belong to the sphere found in part (b)? Justify your answer.
Transcribed Image Text:Work Problem 1. J (a)i- Show that the following equation represents a sphere, and find its center and radius. x² + y² + z² + (-10) x + (−2) y + (−8) z + 38 = 0 (b) Find an equation of the sphere that passes through the point (-2, 0, 1) and centered at the point (0, 1, 1). (c)! Does the point P(3, 1, 0) belong to the sphere found in part (b)? Justify your answer.
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