已知直线L:(m+1)x+(m-1)y-3m-1=0 圆C:x^2+y^2=9 (1)判定直线L与圆的位...

发布网友发布时间：2024-03-31 06:28

共4个回答

热心网友时间：2024-09-18 15:26

(m+1)x+(m-1)y-3m-1=0
(m+1)x+(m-1)y=3m+1
(x+y)m+x-y=3m+1
x+y=3
x-y=1
则x=2，y=1
直线L:(m+1)x+(m-1)y-3m-1=0恒过(2,1)
圆C：x^2+y^2=9
则直线与圆C相交

设AB的中点为N
当圆C：x^2+y^2=9 的圆心O与N的连线ON⊥AB时，AB最小
则N点即(2,1)
向量ON;(2,1)
直线的方向向量就是(-1,2)
直线方程为2x+y-5=0

热心网友时间：2024-09-18 15:26

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热心网友时间：2024-09-18 15:27

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热心网友时间：2024-09-18 15:25

分析：圆心（0,0）半径3.和直线L的方程可得d,d与r的关心进行分类讨论，L交AB，则L为圆C直径