4或4
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分析:通過橢圓長軸所在數(shù)軸分類討論,利用離心率的定義,即可求得m的值,然后求出橢圓的長軸的長.
解答:因?yàn)?img class='latex' src='http://thumb.zyjl.cn/pic5/latex/25951.png' />,
若4>m>0,則a
2=4,b
2=m,∴c
2=a
2-b
2=4-m,∴
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=
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,∴m=2;2a=4
若4<m,則a
2=m,b
2=4,∴c
2=a
2-b
2=m-4,∴
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,∴m=8,2a=4
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∴橢圓的長軸長為:4或4
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.
故答案為:4或4
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點(diǎn)評:本題考查橢圓的離心率,考查分類討論的數(shù)學(xué)思想,考查學(xué)生的計算能力,屬于基礎(chǔ)題.