【福州第一中学】2024-2025学年高二上学期10月月考数学试卷+答案
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第二节(满分25分)One possible versionThen came the Rajasthan /v trip which was our official last trip I hanged out with my otherErieiends while she with the other two girls. I wasn,t enjoying this trip at all, which she could makeBout. When she saw me approaching the common washroom, she followed me in and shut thedoor. I didn 't know how to react. She gave me a tight hug and broke down. My tears were alsoout of control We knew we both wanted to be in each others company. We promised to growmature and let it not affect our friendshipaozIt's been almost 7 years after graduation since we picked up our friendship. Shes one of thefew people I really count on in my life. She's been with me through all my struggles, helping meconstantly to grow into a better individual. So have I. The only learning from our relationshipis-if someone is meant to be in your life, they will ensure they stay around some way or theher Willingness to keep a relationship should come from both the sides
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19解:(1)法一、抛物线的焦点为F(P,0),准线为x=-,设M(x,y),则MF=x+,1分过点M作x轴的垂线,垂足为K,则FK=X22分在R△MFK中,∠MFK=60°,故MF=2XF,即x+B=2x-P),即x=之3分所以y2=2pX0=3p2,故y=√3p4分由SAMOF2OFI=√3,所以p5分所以抛物线C的方程为y2=4x6分法二、抛物线的焦点为F(,0),准线为x=-2,设M(x,y),2则M/=x0+,…1分又因为FM与x轴正方向的夹角为60°,所=Fsin60°=3(x+),…2分所以S△MOF2x=22c+分=、5,所以x=3分43Xt4分248代入y2=2px得=2p(-),解之得p=2或p=2√分又当P=2√3时,FM与x轴正方向的夹角为120°,不符合题意,所以P已2,所以抛物线C的方程为y2=4x+,,6分(Ⅱ1)过N作NO与准线垂直,垂足为O,7分NAlNA则8分M||NeLCosAANO,cos∠MF则当取得最大值时,∠MAF必须取得最大值,此时直线AN与抛物线相切9分设切线方程为y=k(x+1)与y2=4x联立,消去y得kx2+(2k-4)x+k2=0.10分所以Δ=-16k2+16=0,得k=±111分则直线方程为y=x+1成y=-x-1.…:12分写
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