已知过点A(0,1),且斜率为k的直线l与圆c：（x-2)^2+(y-3）^2=1,相交于M,N两点。 1.求实数k的取值范围 2.若O 已知过点A(0,1)且斜率为k的直线l与圆C：(x－2)2＋...
\u5df2\u77e5\u8fc7\u70b9A(0,1),\u4e14\u659c\u7387\u4e3ak\u7684\u76f4\u7ebfl\u4e0e\u5706c\uff1a\uff08x-2)^2+(y-3\uff09^2=1,\u76f8\u4ea4\u4e8eM,N\u4e24\u70b9\u3002\u5982\u56fe\u6240\u793a(\u5f92\u624b\u753b\u7684,\u6709\u70b9\u96be\u770b):
(1)\u5f53k\u4ecb\u4e8ek1,k2\u4e4b\u95f4\u7684\u503c\u5c31\u662f\u6240\u8981\u6c42\u7684K\u7684\u53d6\u503c\u8303\u56f4.\u8bbe\u76f4\u7ebf\u7684\u65b9\u7a0b\u4e3ay-1=k(x-0);\u4e0e\u5706\u65b9\u7a0b(x-2)^2+(y-3\uff09^2=1\u8054\u7acb\u65b9\u7a0b\u7ec4,\u5373\u628a\u76f4\u7ebf\u65b9\u7a0b\u4ee3\u5165\u5706\u65b9\u7a0b\u4e2d\u5f97\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b(k^2+1)x^2-4(k+1)x+7=0(\u4e3a\u4e86\u6b63\u786e,\u8bf7\u697c\u4e3b\u9a8c\u8bc1,\u672c\u4eba\u8ba1\u7b97\u7c97\u5fc3),\u4ee4\u25b3=0,\u89e3\u51fa\u4e24\u4e2ak1,k2\u7684\u503c,\u6240\u4ee5k\u7684\u503c\u5c31\u4ecb\u4e8ek1,k2\u4e4b\u95f4.
(2)\u6b64\u9898\u8f83\u7e41\u7410,\u8981\u7761\u89c9\u4e86,\u6709\u7a7a\u5e2e\u4f60\u89e3\u51b3!
\u8bf7\u91c7\u7eb3
设直线方程为y - 1 = kx
y - kx - 1 = 0
圆心为（2,3），半径为1，所以圆心到直线的距离为
|3 - 2k - 1|/√（k² + 1）
要使直线和圆有两个交点
所以圆心到直线的距离小于半径
|3 - 2k - 1|/√（k² + 1）＜ 1
（2 - 2k）² ＜ k² + 1
4k² - 8k + 4 ＜ k² + 1
3k² - 8k + 3 ＜ 0
所以（4 - √7）/3 ＜ k ＜ （4 + √7）/3
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