已知圆想x2+Y2+X-6Y+M=0与直线x+2y-3=0相交于p,q两点,o为原点,且op垂直于oq,求实数m的值

由x+2y-3=0得x=3-2y代入x2+y2+x-6y+m=0
化简得：5y2-20y+12+m=0y1+y2=4,y1•y2= (12+m)/5
设P、Q的坐标分别为（x1,y1）、（x2,y2）,
由OP⊥OQ可得：x1•x2+y1•y2=0
x1•x2+y1•y2=（3-2y1）•（3-2y2）+y1•y2
=9-6（y1+y2）+5y1•y2
=9-6×4+5× (12+m)/5=m-3=0
解得：m=3