已知圆的方程为x ^2+y ^2+kx+2y+k ^2=0,若定点A(1,2)在圆外,求K的取值范围.

问题描述:

已知圆的方程为x ^2+y ^2+kx+2y+k ^2=0,若定点A(1,2)在圆外,求K的取值范围.

x^2+y^2+kx+2y+k^2=0x^2+kx+(k/2)^2+y^2+2y+1+k^2-(k^2)/4-1=0(x+k/2)^2+(y+1)^2+(3/4)k^2-1=0(x+k/2)^2+(y+1)^2=1-(3/4)k^2圆半径√[1-(3/4)k^2],应有:1-(3/4)k^2≥0,即:k^2≤4/3,解得:-(2√3)/3≤k≤(2√3)/3,...