已知圆x²+y²+x-6y+m=0,和直线x+2y-3=0交于p,Q两点,且op⊥oQ（o为坐标原点）,求该圆的圆心坐标及半径

已知圆x²+y²+x-6y+m=0,和直线x+2y-3=0交于p,Q两点,且op⊥oQ（o为坐标原点）,求该圆的圆心坐标及半径
已知圆x²+y²+x-6y+m=0,和直线x+2y-3=0交于p,Q两点,且op⊥oQ（o为坐标原点）,求该圆的圆心坐标及半径

已知圆x²+y²+x-6y+m=0,和直线x+2y-3=0交于p,Q两点,且op⊥oQ（o为坐标原点）,求该圆的圆心坐标及半径
1.
由余弦定理得
a²=b²+c²-2bccosA
b²+c²-2bccosA=b²+c²+√3ab
cosA=-√3/2
A=5π/6
2.
sinA=sin(5π/6)=1/2
由正弦定理得a/sinA=b/sinB=c/sinC
b=asinB/sinA=2asinB=2√3sinB c=asinC/sinA=2asinC=2√3sinC
S+3cosBcosC
=(1/2)bcsinA +3cosBcosC
=(1/2)(2√3sinB)(2√3sinC)(1/2)+3cosBcosC
=3sinBsinC+3cosBcosC
=3cos(B-C)
当cos(B-C)=1时,S+3cosBcosC有最大值3
此时B=C=(π-5π/6)/2=π/12