Consider the region in the plane bounded by the ellipseand the transformations and(a)
Chapter 14, Problem 31(choose chapter or problem)
Consider the region R in the xy-plane bounded by the ellipse
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
and the transformation x= au and y = bv.
(a) Sketch the graph of the region R and its image S under the given transformation.
(b) Find \(\frac{\partial(x,\ y)}{\partial(u,\ v)}\).
(c) Find the area of the ellipse.
Text Transcription:
x^2 /a^2 + y^2 /b^2 =1
partial (x, y) / partial (u, v)
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