One possible versionThen I wondered whether the man would still be at the same spot. I walked out the doorand back to the street where I had met him. There the man was, at the same spot, knees curledup against his chest, with the same cardboard sign shading his head. I walked down the street,and before I could think twice, I stood before him. He cautiously glanced in my direction.Ismiled and held up the lunch bag. "I brought you some lunch, "I saidI handed him the bag, and he looked closely at it. " Thank you for this. I was praying thismorning, asking for someone,s heart to open. We talked for a little while. As he shared hisstory, there was an, open, honest tone in his voice. There was something about giving thatmade me feel like I was talking with a brother. "I hope you have a nice day, "I told him<"Thank you! It's already gotten a lot better, " he said. As I walked by, his thank fulness hadbecome mind. My day, too, had already gotten a lot better. Anything helps, indeed
19.(1)根据题意知,{a2’,解得a=2c=1.3分由此,b2=3,故椭圆C的标准方程为x y=1分(2)由(1)知,F2(,0),直线AB的斜率不可能为0,因此设直线AB为x=my t(m≠0),与椭圆C联立,得关于y的一元二次方程3m2 4)y2 6mty 32-12=0,16分设A(x1,y1),B(x2,y2),则A(x,-片)根据韦达定理有y1 y23m2 4而AB所在直线经过点F(,0),因此一当,=台1 xx2-y2-y=0等价于2my1y2 (t-1)(V1 y2)=010分将①式代入,得2m(32-12)-(-1)6mt=0,化简得【=4,11分因此直线AB恒过定点(4,0)
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