2. Consider the outer surface of a planet given by x² + y² + z² = 1. There are two cities, one in the Northern Hemisphere located at x = 1/2 and y = 1/2 and one in the Southern Hemisphere located at x = 1/4 and y √11/4 which an see a comet moving across the sky. = (a) Find the tangent planes to the planet at each of the two cities.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Consider the outer surface of a planet given by r? + y² + z² = 1. There are two cities, one in
the Northern Hemisphere located at x = 1/2 and y = 1/2 and one in the Southern Hemisphere
located at æ = 1/4 and y = V11/4 which an see a comet moving across the sky.
(a) Find the tangent planes to the planet at each of the two cities.
(b) The comet travels along a path where the tangent planes intersect, find its trajectory if
it goes through the point y = 0.
Transcribed Image Text:2. Consider the outer surface of a planet given by r? + y² + z² = 1. There are two cities, one in the Northern Hemisphere located at x = 1/2 and y = 1/2 and one in the Southern Hemisphere located at æ = 1/4 and y = V11/4 which an see a comet moving across the sky. (a) Find the tangent planes to the planet at each of the two cities. (b) The comet travels along a path where the tangent planes intersect, find its trajectory if it goes through the point y = 0.
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