英语周报高一2022-2023新课程第40期答案

20.解(1)因为c=2,所以a=①,(1分)依题意A(-a,0),M(-a,b),F(-c,0),所以△AMF的面积S2(a-c)b=即(a-c)2b2=(2-1)②,(2分)又b2=a2-c2③,(3分)解①②③得a=2,b=c=1,(4分)所以椭圆C的方程为x+y2=1.(5分)(2)依题意,直线l的斜率存在且不为0,设其方程为y=k(x+2),代入+y2=1,消去y,得(1+2k2)x2+42k2x+4k2-2=0,(6分)因为A(-,0),可设P(x,),则(-互)x,=4=2,得x=2=2E2,(7分)因为⊥l,且过点B(,0),故可设直线l方程为yA(x-),与y=k(x+2)联立解得Q点的横坐标为x0=2-2k1+k2-(8分)由S1=2S2可得AP|=2|PQ1,所以AP=2PQ,(9分)则xp+=2(x-x),即3x=2x0-2,(10分)所以3×2-22E=2×2-2E-,即3=6=1=31+22-1+k2,(11分)化简得k2=1,所以k=±1所以直线l的斜率k=1或-1.(12分)

书面表达One possible version:NOTICEA sports meeting will be held in the playground of our school from next Thursday to FridayAs you know, the pressure of study is very heavy now, especially for those senior 3. So the purpose of the sports meeting is to letevery student get relaxed, as a result of which we students can live happily and heal thilyEveryone is welcome to take part in it. Those who perform excellently at the sports meeting will get prizes. But don' t take theresults so serously because taking part is more important than the result. Good luck to everyone!

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