x²+y²-4x-2y-8=0
(x-2)²+(y-1)²=13
直线ax+2by=0(a,b大于0)始终平分圆x²+y²-4x-2y-8=0的周长
说明直线过圆心即2a+2b=0即a+b=1
1/a+2/b
=(1/a+2/b)(a+b)
=1+b/a+2a/b+2
>=2√(b/a)(2a/b)+3
=3+2√2
选D
x²+y²-4x-2y-8=0
(x-2)²+(y-1)²=13
直线ax+2by=0(a,b大于0)始终平分圆x²+y²-4x-2y-8=0的周长
说明直线过圆心即2a+2b=0即a+b=1
1/a+2/b
=(1/a+2/b)(a+b)
=1+b/a+2a/b+2
>=2√(b/a)(2a/b)+3
=3+2√2
选D