Consider the set S composed of the points on the line segment S₁ between points (-1,0) and (2,0) and of the points on the line segment S₂ between points (0, -1) and (0,3). We are interested in the optimization problem 2* = min{(2-3)² + a²y² + (y-2)² | (x, y) = S}. Note that * 5 since (x, y) = (2,0) is a feasible solution to this problem. 1. Determine conditions on the values of a, b, c and d for which the set E = {(x, y) = R² | a(x-c)² + b(y-d)² <1} is convex and is such that SCE. 2. Determine the values of a and b that lead to the smallest convex set E₁ = {(x, y) = R² | a(x)² + b(y)² <1} that is such that SCE₁. 3. Determine the values of a and b that lead to the smallest convex set E₂ = {(x, y) = R² | a(x - 1)² + b(y-1)² ≤ 1} that is such that S CE2.

Consider the set S composed of the points on the line segment S₁ between points (-1,0) and (2,0) and of the points on the line segment S₂ between points (0, -1) and (0,3). We are interested in the optimization problem 2* = min{(2-3)² + a²y² + (y-2)² | (x, y) = S}. Note that * 5 since (x, y) = (2,0) is a feasible solution to this problem. 1. Determine conditions on the values of a, b, c and d for which the set E = {(x, y) = R² | a(x-c)² + b(y-d)² <1} is convex and is such that SCE. 2. Determine the values of a and b that lead to the smallest convex set E₁ = {(x, y) = R² | a(x)² + b(y)² <1} that is such that SCE₁. 3. Determine the values of a and b that lead to the smallest convex set E₂ = {(x, y) = R² | a(x - 1)² + b(y-1)² ≤ 1} that is such that S CE2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 41E

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