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In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge of the area of a circle. For example, consider R, the region bounded by the (x+3)² (y − 2)² 16 ellipse 9 √ [₁₁A= √ √ 8 will make the tranformation, (x, y) d(u, ‚v) S dA region S is bounded by u²+ v² This means, we must let U= V= X = + = = 1. For easy calculation, we leading to a Jacobian of -dudu, where the transformed which should be easily inverted to obtain = = 1, d(x, y) 0(u, v) and and We calculate the area of the ellipse by multiplying the area of the unit circle and the Jacobian, arriving at (give an exact answer)

In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge of the area of a circle. For example, consider R, the region bounded by the (x+3)² (y − 2)² 16 ellipse 9 √ [₁₁A= √ √ 8 will make the tranformation, (x, y) d(u, ‚v) S dA region S is bounded by u²+ v² This means, we must let U= V= X = + = = 1. For easy calculation, we leading to a Jacobian of -dudu, where the transformed which should be easily inverted to obtain = = 1, d(x, y) 0(u, v) and and We calculate the area of the ellipse by multiplying the area of the unit circle and the Jacobian, arriving at (give an exact answer)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 33E
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In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge of the area of a circle. For example, consider R, the region bounded by the (x+3)² (y-2)² = 1. For easy calculation, we 16 ellipse 9 √ [₁₁A= √ √ 8 will make the tranformation, (x, y) d(u, ‚v) S dA region S is bounded by u²+ v² This means, we must let U= V= x = + = -dudv, where the transformed leading to a Jacobian of which should be easily inverted to obtain = = 1, a(x, y) 0(u, v) and and We calculate the area of the ellipse by multiplying the area of the unit circle and the Jacobian, arriving at (give an exact answer)
Transcribed Image Text:In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge of the area of a circle. For example, consider R, the region bounded by the (x+3)² (y-2)² = 1. For easy calculation, we 16 ellipse 9 √ [₁₁A= √ √ 8 will make the tranformation, (x, y) d(u, ‚v) S dA region S is bounded by u²+ v² This means, we must let U= V= x = + = -dudv, where the transformed leading to a Jacobian of which should be easily inverted to obtain = = 1, a(x, y) 0(u, v) and and We calculate the area of the ellipse by multiplying the area of the unit circle and the Jacobian, arriving at (give an exact answer)
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