已知圆C过定点A（0,P）（P为正数,圆心C在抛物线X=2Py上运动,若MN为圆C在X轴上截得的弦,设AM=L1,AN=
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已知圆C过定点A（0,P）（P为正数,圆心C在抛物线X^2=2Py上运动,若MN为圆C在X轴上截得的弦,设AM=L1,AN=L2,〈MAN=θ （1）当C点运动时,MN是否变化,并证明（2）求式子L2/L1+L1/L2的最大值,并求取得此最大值时θ的值和此圆的方程
设圆心（2t,2tt/p）
(x-2t)^2+(y-2tt/p)^2=rr
过定点A（0,P)
4tt+pp+4tttt/pp-4tt=rr
pp+4tttt/pp=rr
(x-2t)^2+(y-2tt/p)^2=rr
(x-2t)^2+4tttt/pp=rr=pp+4tttt/pp
(x-2t)^1=ppx1=2t+px2=2t-pMN=2p定值当C点运动时MN不变化=2P
L1L1=4tt+2pp+4tp
L2L2=4tt+2pp-4tp
L1L1+L2L2=MNMN+2L1L2cosθ
s=L2/L1+L1/L2
ss-2=(4tt+2pp+4tp)/(4tt+2pp-4tp) +(4tt+2pp-4tp)/(4tt+2pp+4tp)
=2+8tp/(4tt+2pp-4tp) -8tp/(4tt+2pp+4tp)
=2 +8tp(8tp)/(4tt+2pp-4tp) (4tt+2pp+4tp)
=2+16pp *tt/(2tt+pp-2tp) (2tt+pp+2tp)
=2+16pp/(2t +pp/t -2p)(2t +pp/t +2p)
<=2+16pp/(2genhao2p -2p)(2genhao2p +2p)=6
L2/L1+L1/L2的最大值=6
当2t =pp/t时取到
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