Question

求圆心在直线2x+y=0上,且与直线x+y+1=0切于点A(-2,1)的圆的标准方程.

Answer 1

设圆心O坐标是(m,-2m)

圆的标准方程是(x-m)^2+(y+2m)^2=r^2

圆心O到直线x+y+1=0的距离=r

即 |m-2m+1|/根号2=r (1)

点A(-2,1)在圆上,即(-2-m)^2+(1+2m)^2=r^2 (2)

联立(1)(2)

解得m=-1,r^2=2

圆的标准方程是(x+1)^2+(y-2)^2=2