高中数学一圆与两条平行直线问题 只有图片一张最好解析一下

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 = -1/3
(sinA/cosA)^2 = 1/9
9*(sinA)^2 = (cosA)^2 = 1 - (sinA)^2
sinA = 1/√10
R = (5 - 3)/2*sinA = 1/√10
圆方程：
(x + 7/5)^2 + (y - 13/5)^2 = R^2
10(x + 7/5)^2 + 10(y - 13/5)^2 = 1
（x+7/5）^2+(y-13/5)^2=1/10