2022英语周报外研高一2答案

4-2-(2)21.解:(1)由题知,3)2(2解得b2=1,所以椭圆C的方程为+y2=1(4分)(2)由题意知直线l的斜率存在,设为k,建点A(-2,0),则Z的方程为y=k(x+2)联立消去y,y=k(x+2),整理得(1+42)x2+16k2x+16k2-4=0,(6分)显然△=(16k2)2-4(1+4k2)(16k2-4)=16>0恒成立令B(xB,yB),C(0,yc),由-2xB=1+42·得x8≈2-8k216k-41+4k2(8分)将x=0代入y=k(x+2)中,得到y=2k,所以|OC|=|2k,BC|=√+k|x0-0=+k1|2=8由0C=1BC,得2=计k4(10分)解得k2=1所以k=士所以直线L的斜率为士(12分)4

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