1楼:甐芅慂
设a(x1
,)、b(x2,y2),
则设p(x,y)为过a的切线上一点,可得
ap=(x-x1,y-y1)∵ap
?oa=0,得x1(x-x1)+y1(y-y1)=0,化简得x1x+y1y=x1
2+y1
2∵点a在圆x2+y2=r2上,可得x1
2+y1
2=r2
∴经过点a的圆的切线为x1x+y1y=r2,同理可得经过点b的圆的切线为x2x+y2y=r2.又∵点p(x0,y0)是两切线的交点,
∴可得x0x1+y0y1=r2,说明点a(x1,y1)在直线x0x+y0y=r2上;
同理x0x2+y0y2=r2,说明点b(x2,y2)在直线x0x+y0y=r2上
因此可得直线ab方程为:x0x+y0y=r2故答案为:x0x+y0y=r2