已知椭圆ax²+by²=1与直线x+y-1=0交AB两点,|AB|=2分之根号2,AB的中点M与椭圆中心的连线的斜率为2分之根号2,求椭圆方程.
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![已知椭圆ax²+by²=1与直线x+y-1=0交AB两点,|AB|=2分之根号2,AB的中点M与椭圆中心的连线的斜率为2分之根号2,求椭圆方程.](/uploads/image/z/10109408-32-8.jpg?t=%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86ax%26sup2%3B%2Bby%26sup2%3B%3D1%E4%B8%8E%E7%9B%B4%E7%BA%BFx%2By-1%3D0%E4%BA%A4AB%E4%B8%A4%E7%82%B9%2C%7CAB%7C%3D2%E5%88%86%E4%B9%8B%E6%A0%B9%E5%8F%B72%2CAB%E7%9A%84%E4%B8%AD%E7%82%B9M%E4%B8%8E%E6%A4%AD%E5%9C%86%E4%B8%AD%E5%BF%83%E7%9A%84%E8%BF%9E%E7%BA%BF%E7%9A%84%E6%96%9C%E7%8E%87%E4%B8%BA2%E5%88%86%E4%B9%8B%E6%A0%B9%E5%8F%B72%2C%E6%B1%82%E6%A4%AD%E5%9C%86%E6%96%B9%E7%A8%8B.)
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