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
icon
Related questions
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  x2+8xy+17y21.

Use the change in variables s=x+4y and t=y

Or y=t and x=s4t

Hence, the required area is given by

Area=dxdy=Jdsdt

Where, J=Jacobian

Now,

J=dxdsdxdtdydsdydt=1401=1

Hence, J=1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,