【摘 要】
：
<正>问题已知椭圆x~2/4+y~2=/31,O为原点,过椭圆的右焦点F的直线l交椭圆于A、B两点,求△OAB面积的最大值.此题是椭圆中三角形面积的典型例题,其中三角形的一个顶点在原点,另
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<正>问题已知椭圆x~2/4+y~2=/31,O为原点,过椭圆的右焦点F的直线l交椭圆于A、B两点,求△OAB面积的最大值.此题是椭圆中三角形面积的典型例题,其中三角形的一个顶点在原点,另两个顶点在椭圆上.题目表述简洁明了,初看非常平淡,实则内涵丰富.通过活用直线、椭圆的各种方程,多角度探究解法、背景、推广,能得到一些有用的结论,值得细思赏玩.
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