若直线2ax-by+2=0(a,b>0),始终平分圆x2+y2+2x-4y+1=0的周长,则
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由于直线2ax-by+2=0(a,b>0),始终平分圆x2+y2+2x-4y+1=0的周长,
故直线直线2ax-by+2=0必过x2+y2+2x-4y+1=0的圆心(-1,2),
则-2a-2b+2=0,即a+b=1,
所以
+1 a
=(1 b
+1 a
)(a+b)=2+1 b
+b a
≥2+2a b
=4
×b a a b
故答案为 A
若直线2ax-by+2=0(a,b>0),始终平分圆x2+y2+2x-4y+1=0的周长,则
|
由于直线2ax-by+2=0(a,b>0),始终平分圆x2+y2+2x-4y+1=0的周长,
故直线直线2ax-by+2=0必过x2+y2+2x-4y+1=0的圆心(-1,2),
则-2a-2b+2=0,即a+b=1,
所以
+1 a
=(1 b
+1 a
)(a+b)=2+1 b
+b a
≥2+2a b
=4
×b a a b
故答案为 A