过圆:x2+y2 r2外一点P(x0,y0)引此圆的两条切线

2021-01-12 17:00:34 字数 442 阅读 6430

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