In the following exercises, the transformation \(T: S \rightarrow R, T(u, v)=(x, y)\) and the region \(R \subset \mathrm{R}^{2}\) are given. Find the region \(S \subset \mathrm{R}^{2}\).

x = au, y = bv, \(R=\left\{(x, y) \mid x^{2}+y^{2} \leq a^{2} b^{2}\right\}\) where a, b > 0

Text Transcription:

T: S rightarrow R, T(u, v)=(x, y)

R subset R^2

S subset R^2

x=a u, y=b v, R={(x, y) |x^2+y^2 leq a^2 b^2}

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