过点P(2,3)且与圆x2+y2=4相切的直线方程是(  ) A.2x+3y=4 B.x=2 C.5x-12y+26=0 D.5x-12y+26=0x=2

问题描述:

过点P(2,3)且与圆x2+y2=4相切的直线方程是(  )
A. 2x+3y=4
B. x=2
C. 5x-12y+26=0
D. 5x-12y+26=0x=2

由题意可得点P(2,3)在圆x2+y2=4外面当切线的斜率不存在时,此时的直线方程为x=2满足条件当直线的斜率存在时设为k,则切线方程为y-3=k(x-2)根据直线与圆相切可得圆心(0,0)到直线的距离d=|3−2k|1+k2=2k=512...