Using an Ellipse Consider the region in the plane bounded by the ellipse and the
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 transformations 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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