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.
问题描述：
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.
答
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^2b^2 = 7 r^2又 a^2 + b^2 = r^2 ,a^2 = 9 b^210 b^2 = r^2 = 1/7 b^2b^2 = 7/69 ,a^2 = 63/69 ,r^2 = 1/69圆的方程为 ...