Question

已知关于x,y的方程C:x2+y2-4x+2y+m=0.若圆C与直线L:2x-y-4=0相交于M,N两点,且MN=6/根

Answer 1

解方程组得

x =

8/5+1/5*(24-5*m)^(1/2)

8/5-1/5*(24-5*m)^(1/2)

y =

-4/5+2/5*(24-5*m)^(1/2)

-4/5-2/5*(24-5*m)^(1/2)

再用两点间距离公式得

(96/5-4*m)^0.5=6/5^0.5

m=3