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(2017•新课标Ⅱ)设O为坐标原点,动点M在椭圆C: x22 +y2=1上,过M做x轴的垂线,垂足为N,点P满足 NP→ = 2NM→ .
(Ⅰ)求点P的轨迹方程;
(Ⅱ)设点Q在直线x=﹣3上,且 OP→ • PQ→ =1.证明:过点P且垂直于OQ的直线l过C的左焦点F.