求由点A(3,2)向圆x²+y²-4x+2y-4=0引切线,切点与点A的距离
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求由点A(3,2)向圆x²+y²-4x+2y-4=0引切线,切点与点A的距离
求由点A(3,2)向圆x²+y²-4x+2y-4=0引切线,切点与点A的距离
求由点A(3,2)向圆x²+y²-4x+2y-4=0引切线,切点与点A的距离
提示:点A与切点间线段、圆心与点A间线段、圆心与切点间线段构成直角三角形.
整理圆方程得
(x-2)²+(y+1)²=9
圆心坐标(2,-1),圆半径=3,设切点B
OB=圆半径=3 OA=√[(2-3)²+(-1-2)²]=√10
所求距离=AB=√(OA²-OB²)=√(10-9)=1