试题与答案

若对于给定的正实数k，函数f(x)=kx的图象上总存在点C，使得以C为圆心，1为

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题型：填空题

题目：

若对于给定的正实数k，函数f(x)=
k
x
的图象上总存在点C，使得以C为圆心，1为半径的圆上有两个不同的点到原点O的距离为2，则k的取值范围是______．

答案：

根据题意得：|OC|＜1+2=3，

设C（x，

k
x
），

∵|OC|=

x2+
k2
x2
≥
2k
，

∴

2k
＜3，即k＜
9
2
，

则k的范围为（0，

9
2
）．

故答案为：（0，

9
2
）

考点：直线与圆的位置关系
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题型：完形填空

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