英语周报高考英语2021-2022第四期答案

21.解:(1)设点D(x,y),P(x,y),则Q(x2,0),ab=(x-x,y),Q声=(0,y),因为b=2@声,=0所以即y=2yo,=2因为点P在椭圆C上,所以 =1,即为点D的轨迹方程,又因为点D轨迹是过点(0,2)的圆,所以4=1,解得/a=4,b2±1所以椭圆C的方程为x y2=1(5分)(2)设直线AN的方程为y=k1x 1,直线AM的方程为y=k2x 1不妨设k1>0,则k2<0, y2=1由y=k1x 1,得(1 4k)x2 8k1x=0,解得xN4k 1同理xM=~、8k2(7分)日因为M,O,N三点共线,则由xM xN=4 14k =0整理得(k1 k2)(4k1k2 1)=0,当k1 k2=0时,易得E(-4,3),F(4,3),S3×8=12,(8分)当k1·k2时令y=3得E(2,3),P(2,3)而yN=k1xN 1=4k 14k2 14k 1所以△ENF的面积S△E=2×EF×(3-y)2(2-2)(计 )一· (10分)由kk2=一4得k2=-4k1则S△BP=过 1.16816k1 2≥8√2,当且仅当k=时取等号,所以△ENF的面积的最小值为8√2(12分)

第三节One possible versionParagraph 1Finally, afler struggling for a minute or tuo, I still gotpulled underwater. I told myself I should never give upThen I pulled the weed again with great efforts. The weedfinally broke. I swam back to the surface to take a debreath. I saw two young men in canoes, racing each other.I was exhausted and shouted for help. The two men saw meand raced towards me. By the time they reached me, I hadbeen already unconsciousParagraph 2When woke up, I was in an empty room lying on abed. It was not until a doctor came into the room that I realized that I was in a hospital. Jimmy and Bobby told me thetwo young men brought me to the shore and sent me to thehospital. After a few minutes, my parents with half angryand half worried faces walked in. My parents scolded me ifor running out of the house secretly but were also glad thatI was not seriously injured. I will never forget that terrifyingexperience. Neither will I ever want to show off again

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