Use the change in variables s = x + 4y, t = y to find the area of the ellipse x^2 + 8xy + 17y^2, less than or equal to 1.
Use the change in variables s = x + 4y, t = y to find the area of the ellipse x^2 + 8xy + 17y^2, less than or equal to 1.
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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Question
Use the change in variables
s = x + 4y, t = y to find the area of the ellipse
x^2 + 8xy + 17y^2, less than or equal to 1.
Expert Solution
Step 1
We have to find the area of the ellipse .
Use the change in variables
Or
Hence, the required area is given by
Where, Jacobian
Now,
Hence,
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