圆E:x2+y2-x-6y+m=0与直线l:x+2y-3=0交于P、Q两点,O是坐标原点,若OP垂直OQ,求m的值;若E

x+2y-3=0x=3-2y,代入圆E方程,整理得：5y^2-16y+6+m=0 y1+y2=16/5 y1y2=(6+m)/5x1x2=(3-2y1)(3-2y2) =9-6*16/5+4(6+m)/5 =(4m-27)/5(1)OP*OQ=0 x1x2+y1y2=0 (4m-27)/5+(6+m)/5=0 m=21/5(2)EP*EQ=0 E:(x-1/2)^2+(y-3)^2=37/4-m E(1/2,3) EP=(x1-1/2,y1-3) EQ=(x2-1/2,y2-3) (x1-1/2)(x2-1/2)+(y1-3)(y2-3)=0 x1x2-(x1+x2)/2+1/4+y1y1-3(y1+y2)+9=0 m=87/20