=52解折】1)题意可知{b=2.-如=1,(3分)2=a2-b2故椭圓C的标准方程为+y2=1,………(4分)OA·OB5×1=√3AB…(5分)√6(2)设P(x·%),切线PM,PN的斜率分别为k1,k2,过点O的切线方程为kx-y=0,则n二=×0√=6,整理,即(6d-5)42-120k+63后-5=0,……(6分)k+k=6-一5根据韦达定理可知(7分)k2=51=55+=1文化故y=16.x099=9y66x6-5632-5(8分)OP的最小值为OB=1>n,故点O总在⊙P外,此方程△>0恒成立OM·OE·sin∠MCEA==AME………………………………(9分)ON:OD·sin∠NOD设D(x,y),E(x2,y)∵hk=当=一1,:25的=nn,12又ⅵ=1-互y=12(1-5)(1-)-rix,整理得:x+x=5,…………(10分)∴E2+OD=x+y+n+y=2+(x+n)=6,且易知OD∈(b,a),即1

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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