Question

直线l：x+2y-3=0与圆C：x²+y²+x-6y+m=0有两个交点A、B,O为坐标原点,若向量O

Answer 1

x+2y-3=0(1)

x^2+y^2+x-6y+m=0(2)

x=3-2y(3)

把（3）带入（2）

（3-2y)^2+y^2+3-2y-6y+m=0

5y^2-20y+12+m=0

A(x1,y1)B(x2,y2)

y1+y2=4,y1y2=(12+m)/5

x1x2+y1y2=0

(3-2y1)(3-2y2)+y1y2=0

9-6y2-6y1+4y1y2+y1y2=0

9-6(y1+y2)+5y1y2=0

9-6x4+5x(12+m)/5=0

m=3