衡中同卷·2023届调研卷 全国卷B 文综(四)4数学试卷答案(更新中)

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【短文改错】Today we made paper airplane.Our teacher said,"We will see which airplane flies the farther."Ofairplanesfarthestcourse,I wanted mine to fly farther than A other airplanes.We stood at the front of the elass and took turnsthethrowour airplanes.The teacher had a ruler.She measured what far each airplane travelled.throwing/或throw前加tohowSome airplanes did not go far,which it flew only two metres and then fall to the floor.Most travelled seven orfelleight metres.It was her turn.I stood at the starting line but I threw it as hard as I was able to.I eager watched it flymyandcagerlyhigh above the floor.After about six seconds,it landed at the back of the room.“Ten metres！”said our teacher.

21【解折X(DsinPF,R-合PF+PF,=a,PR=a,PF=号，：PE2+|rE2=|Ps|,ER=2,∴a=Ec,d=C十1c=1,a=反椭圆方程为：号十y=1.。…(4分[另解]设Pc,w),代入描圆方程，由心=+1，解得PE=0=日，inPE.F.PFP1+1 PF.小树圆方程为：号十=1y=kz-1)动直线1的方程为：y=kx一了，由若+=1得(2+1)2-x-6=0,37-9Ak设A(mM),B(2,),则4十=3(2k+1)=一169(2k2+1)4=9+g1+202)16+>0.……(6分)由对称性可设存在定点M(0,m)满足题设，则MA=(1,y一m),MB=(x2,2一m),MA.Mi=0→>x2十(M-m)(2-m)=0>(1+)西-号+m(a十)+（号+m)=-0→6(m2-1)k2+(3m2+2m-5)=0,(9分)由题意知上式对Hk∈R成立，.∴.m2-1=0且3m十2m-5=0,解得m=1.(11分)'.存在定，点M,使得以AB为直径的圆恒过这个点，且，点M的坐标为(0,1).(12分)