2022 英语周报 高三 XN 35答案

第一节Dear Mr GeorgeI am Li Hua, a volunteer of the activity"Englishi Communication to the Mountains". Now, I'm writing toexpress my sincere apology to you for not being present atthe activity to be held next Monday.The reason for my absence is that I suddenly fell illMy parents sent me to hospital, and I have to stay therefor a week. As for my volunteer work, I have asked myclassmate Tom to do it.Sincerely hoping that you can accept my apologiesYours.Li Hua

19.【解析】(1)将圆C的方程配方得:(x-2m)2+(y-m)2=4,所以其圆心为C(2m,m),半径为2.由题设知,椭圆的焦距2c等于圆C的直径,所以c=2所以a=3,从而b2=a2-c2=5,故椭圆E的方程为+=1.3分(2)因为F1,F2关于l的对称点恰好是圓C的一条直径的两个端点所以直线l是线段OC的垂直平分线(O是坐标原点),故l方程为与y2=2x联立得:2y2+2py-5pm=0,由其判别式△m>0,①设A(x1,y),B(x2,y2),则y+y=-p,yy从而x1+x2x(x2=4p162因为F1的坐标为(-2,0A=(x1+2,y),FB=(x2+2,y)注意到FM与F向同N与F同向,所以点F1在以线段MN为直径的圆内台F1M·F1N<0F1A·F1B<08分台(x1+2)(x2+2)+yy<0台x1x2+2(x+x)+4+yy<0台m2+10(2-p)m+4(p+4)<0,②当且仅当Δ=100(2-p)-100(p+4)>0,即p>5时,总存在m,使②成立又当p>5时,由韦达定理知方程m2+10(2-p)m+4(p+4)=0的两根均为正数,故使②成立的m>0,从而满足①故存在数集D=(5,十∞),当且仅当p∈D时,总存在m,使点F1在以线段MN为直径的圆内.……12分

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