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如圖所示,已知圓C:(x+1)
2+y
2=8,定點(diǎn)A(1,0),M為圓上一動(dòng)點(diǎn),點(diǎn)P在AM上,點(diǎn)N在CM上,且滿足AM=2AP,NP⊥AM,點(diǎn)N的軌跡為曲線E.
(1)求曲線E的方程;
(2)若過定點(diǎn)F(0,2)的直線l交曲線E于不同的兩點(diǎn)G、H(點(diǎn)G在點(diǎn)F、H之間),且滿足
FG=FH,求直線l的方程;
(3)設(shè)曲線E的左右焦點(diǎn)為F
1,F(xiàn)
2,過F
1的直線交曲線于Q,S兩點(diǎn),過F
2的直線交曲線于R,T兩點(diǎn),且QS⊥RT,垂足為W;
(�。┰O(shè)W(x
0,y
0),證明:
+<1;
(ⅱ)求四邊形QRST的面積的最小值.