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Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0) and give the corresponding minimum distance.

Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0) and give the corresponding minimum distance.

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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PART B: Find the two (, y, z) points on the surface z? = x² + 3y² that are closest to the point (2, 2, 0) and give the corresponding minimum distance. Clearly set up a two-variable function for distance, show work in solving for critical point(s) and stop. You do NOT have to use the 2nd derivative test and you do NOT have to prove you have a minimum. Type this below: " min dist = ? at (?, ?, ?) and (?, ?, ?) " %3D Replacing the "?" with your answers (order of points doesn't matter).
Transcribed Image Text:PART B: Find the two (, y, z) points on the surface z? = x² + 3y² that are closest to the point (2, 2, 0) and give the corresponding minimum distance. Clearly set up a two-variable function for distance, show work in solving for critical point(s) and stop. You do NOT have to use the 2nd derivative test and you do NOT have to prove you have a minimum. Type this below: " min dist = ? at (?, ?, ?) and (?, ?, ?) " %3D Replacing the "?" with your answers (order of points doesn't matter).
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