Point on an Ellipse Farthest from a Given Point

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2017-10-26 22:37

① This example demonstrates how to find the point on an ellipse that is farthest from an external given point, and dynamically shows the farthest point and the distance segment. ② Core mathematical concepts include the parametric equation of an ellipse, the distance formula between two points, and optimization of a distance function, often solved by differentiation or geometric reasoning. ③ Construction details: using GeoGebra commands Intersect to find intersection points, Point to define the given point, Distance to compute the distance, Segment to connect the farthest point with the given point, and LaTeX text to display the distance value; objects include ellipse c, points A and B, distance d, segment L, and multiple text labels. ④ Suitable for high school or early college students to understand extremum problems on conic sections, and as a visual aid for calculus optimization concepts.

GeoGebra Commands & Parameters

Intersect(c, xAxis, 2) → A
Point(c) → B
Distance(A, B) → d
Segment(A, B) → L
LaTeX(d, true, true) → text3
LaTeX(B, true, true) → text4

AI Drawing Prompt Reference

Draw an ellipse and mark the point on the ellipse farthest from an external point, dynamically showing the distance line segment between the farthest point and the given point, with the distance value labeled. First find the two intersection points of the ellipse with the x-axis, then determine a point on the ellipse, calculate the distance between these two points, draw the line segment connecting them, and finally display the distance value and the point on the ellipse.

The prompt above was compiled from the original drawing commands and is for reference only.