若直线ax+by-2=0(a>0,b>0)平分圆x2+y2-2x-2y=0,则:(1)a,b满足的条件是______;(2)1a+4b的最小值是______.-数学

题目简介

若直线ax+by-2=0(a>0,b>0)平分圆x2+y2-2x-2y=0,则:(1)a,b满足的条件是______;(2)1a+4b的最小值是______.-数学

题目详情

若直线ax+by-2=0(a>0,b>0)平分圆x2+y2-2x-2y=0,则:
(1)a,b满足的条件是______;
(2)
1
a
+
4
b
的最小值是______.
题型:填空题难度:中档来源:不详

答案

(1)圆心坐标(1,1),直线平分圆,则有圆心在直线ax+by-2=0上,即a+b=2.
(2)因为(a>0,b>0),
所以class="stub"1
a
+class="stub"4
b
=(class="stub"1
a
+class="stub"4
b
)•class="stub"a+b
2
=class="stub"5
2
+class="stub"2a
b
+class="stub"b
2a
≥class="stub"5
2
+2=class="stub"9
2
(当且仅当b=2a时取等号)
故答案为:(1)a+b=2 (2)class="stub"9
2

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