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Max Area Rectangle in Ellipse

Max Area Rectangle in Ellipse
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2019-04-21 01:16
Coordinate GeometryOptimization
This example demonstrates finding the largest rectangle area within an ellipse using GeoGebra, involving the Lagrange Multiplier method, optimization problems, and ellipse geometry. Key commands like Segment and objects a, b, c, u, f, g, h are used for construction. Suitable for high school and above learning optimization and calculus applications.

GeoGebra Commands & Parameters

  1. Segment((a / sqrt(2), b / sqrt(2)), (((-a)) / sqrt(2), b / sqrt(2))) → u
  2. Segment((a / sqrt(2), b / sqrt(2)), (a / sqrt(2), ((-b)) / sqrt(2))) → f
  3. Segment((((-a)) / sqrt(2), b / sqrt(2)), (((-a)) / sqrt(2), ((-b)) / sqrt(2))) → g
  4. Segment((((-a)) / sqrt(2), ((-b)) / sqrt(2)), (a / sqrt(2), ((-b)) / sqrt(2))) → h