Question

圆与y轴相切,圆心在直线x-3y=0上,且在直线y=x上截得的弦长为2倍更好根号7,求此圆的方程.

Answer 1

设圆心坐标A(a ,b),半径为r,a - 3b= 0

圆心到直线y = x的距离为|a - b|/2 = |b|

(|b|)^2 + 7 = r^2

b^2 = 7 r^2

又 a^2 + b^2 = r^2 ,a^2 = 9 b^2

10 b^2 = r^2 = 1/7 b^2

b^2 = 7/69 ,a^2 = 63/69 ,r^2 = 1/69

圆的方程为 63x + 7y = 1