已知点P(1,2)在圆C:x2+y2+kx+2y+k2=0的外部,则实数k的取值范围是________.

已知点P(1,2)在圆C:x2+y2+kx+2y+k2=0的外部,则实数k的取值范围是________.

答案

思路解析:首先把已知圆的方程化为标准式(x+)2+(y+1)2=1-k2,

要使该方程表示圆,首先满足1-k2>0,即k2.

还要满足(--1)2+(-1-2)2>1-k2.

解之,得-<k<.

答案:-<k<

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