已知斜率为-2的直线与椭圆 C: x 2 a 2 + y 2 =1(a>0) 交于A,B两点,且线段AB的中点为 E( 1 2 , 1 2 ) .直线l 2 与y轴交于点M(0,m)(m≠0),与椭圆C交于相异两点P,Q,O为坐标原点,且 PM =λ MQ , OP +λ OQ =4 OM ,λ∈R . (1)求椭圆C的方程; (2)求λ的值; (3)求m的取值范围.
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