sin∠MF2F1=|MF1|/|MF2|=1/3
令x=-c，那么c²/a²-y²/b²=1，∴y=±b²/a，∴|MF1|=b²/a
而|MF2|-|MF1|=2a，∴|MF2|=b²/a+2a
∴(b²/a)/(b²/a+2a)=1/3
∴a=b
∴c=√2*a
∴e=c/a=√2、
故选A
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