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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 (x-4)² (y-2)² 16 1 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes which should be easily inverted to obtain leading to a Jacobian of a (x, y) d(u, v) and v = And since ² √√₁₂₁A = √√₁₂ ₁ a (x, y) a(u, v) calculate the area by multiplying the area and the Jacobian, arriving at (give an exact answer) and y dudu where the transformed region S is bounded by u² + ² = 1, we

In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (x-4)² (y-2)² 16 1 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes which should be easily inverted to obtain leading to a Jacobian of a (x, y) d(u, v) and v = And since ² √√₁₂₁A = √√₁₂ ₁ a (x, y) a(u, v) calculate the area by multiplying the area and the Jacobian, arriving at (give an exact answer) and y dudu where the transformed region S is bounded by u² + ² = 1, we

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 46E
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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 (x-4)² 16 (y-2)² 1 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes U = which should be easily inverted to obtain x = leading to a Jacobian of a (x, y) a(u, v) And since e and v = = and y + a(x, y) • Sf. ₁A = [₁ 0(4,0) dA a(u, v) calculate the area by multiplying the area and the Jacobian, arriving at (give an exact answer) dudu where the transformed region S is bounded by u²+² = 1, we
Transcribed Image Text:In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (x-4)² 16 (y-2)² 1 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes U = which should be easily inverted to obtain x = leading to a Jacobian of a (x, y) a(u, v) And since e and v = = and y + a(x, y) • Sf. ₁A = [₁ 0(4,0) dA a(u, v) calculate the area by multiplying the area and the Jacobian, arriving at (give an exact answer) dudu where the transformed region S is bounded by u²+² = 1, we
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