一圆与两条平行直线x+3y-5=0和x+3y-3=0都相切,圆心在直线2x+y+1=0上,求该圆的方程.

x + 3y - 5 = 0,x + 3y - 3 = 0 是平行线,所以圆心在两条直线中间那条平行线上：x + 3y - 4 = 0 x + 3y = 4 2x + y = -1 联立得到圆心坐标：x = -7/5 y = 13/5 圆半径等于两条直线距离之半,注意到斜率 K = -1/3 tgA ...