给定一椭圆和它的一条定长的动弦,探求以动弦为一边,另一个顶点为椭圆中心的三角形面积的最大值是一个有意义的问题,本文给出这类问题的一种浅显的解法.首先给出下面的引理.引理AB是椭圆b~2x~2+a~2y~2=a~2b~2(a>b>0)的一条弦,c为半焦距,d为椭圆中心到弦AB所在直线的距离,若弦AB的倾斜角为θ,记,f(θ)=a~2-c~2cos~2θ,则 Given an ellipse and its fixed-length chord, exploring the maximum value of the area of ​​the triangle with the chord as the side and the other vertex as the center of the ellipse is a meaningful problem. This article gives a brief explanation of this type of problem. The solution is to first give the following lemma. Lemma AB is a string of ellipses b~2x~2+a~2y~2=a~2b~2(a>b>0), where c is the semifocal length, d The distance from the center of the ellipse to the line where the string AB is located, if the angle of inclination of the string AB is θ, note that f(θ) = a~2-c~2cos~2θ, then