20.[命题立意]考查椭圆的方程,抛物线的方程,直线与椭PAB所成锐圆的位置关系,范围问题;考查逻辑推理,数学运算的核心素养[试题解析](1)设椭圆C1的焦距为2c,由题意得a=2,则抛物线G:y2=4x,将x=C代入y2=4ax,得以4即(2由所以b=√3,p=4所以椭圆C1的标准方程为+2=1,抛物线C2的标准方程为y2=8x(4分)(2)设直线PQ的方程为x=my+1,P(x1,y1),Qx2,y2)由+3=1,消去x,得(m+4y+my-9=0故y1.y1 J2所以PQ=√1+mby-y|=√1+m√(y+y)-412(1+m2)(6分)当m≠0时,直线FT的方程为y令x=4,得T(4,-3m),所以|TF1=3√1+m1=3112(1+m2)(3√1+m2+3m2+41所认1PQ3√1+,12(1+m25)=4(3√1+m2+1+m(8分)令1=√1+m,>1,则TF13xPQ=44+42令f(t),t∈(1,+∞)3-1=31>0所以f(1)=4-4242所以f(t)在(1,+∞)上是增函数,所以f(1)>f(1)=1,PQ-1I TFI(10分)当m=0时,F(1,0),T(4,0),所以TF|=3,PQ=3,所以综上所述,TF1PQ的取值范围是[1,+∞).(12分)

读后续写Possible version lI stared at the paper and then looked around. I was cold. Although I could not see my sistersnor the new house, which was hidden from my sight by a grey wall, I got the feeling that I was notalone. Walking along the shore was a tall familiar figure who looked lost in his thoughts. I lookedgain at the paper in my hand, closed my eyes and wishedAs /opened my eyes, I found my father was standing right beside me. Happy birthday, sonhe said, patting my shoulder gently. I smiled up at him and took his hand. Looking back, life fromthat day on marked the start of a close bond and a strong friendship with my father. What was mybirthday surprise? Wishes do come truePossible version 2I stared at the paper and then looked around. On the backside, there was a map. I noticed thatit was clearly leading me in a direction, but who could have sent this? I stood there in silence andstudied it. I decided to follow the map and it led me down the beach until I reached a staircase. Iooked back and could no longer see my siblings. I continued to follow the point on the map, untilI unexpectedly lost my footing and fell zksq down the stepsAs I opened my eyes, I found my father was standing right beside me. Happy birthday, sonhe said, patting my shoulder gently. Then he asked how I had come upon this place? I explained tohim that I had found the bottle in the ocean and when I opened it had the words on it. Shocked bythe message, my father realized what I had found I threw this bottle into the ocean many years agowhen I was alone. he said. I used to come to this exact place to get away from everyone else. NowI get to share this experience with you. What a birthday surprise

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