已知直线5x-12y+a=0与圆x^2-2x+y^2=0相切,则a的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 03:53:37
已知直线5x-12y+a=0与圆x^2-2x+y^2=0相切,则a的值

已知直线5x-12y+a=0与圆x^2-2x+y^2=0相切,则a的值
已知直线5x-12y+a=0与圆x^2-2x+y^2=0相切,则a的值

已知直线5x-12y+a=0与圆x^2-2x+y^2=0相切,则a的值
直线5x-12y+a=0与圆x^2-2x+y^2=0相切
5x - 12y + a = 0,
y = (5x+a)/(12),
x^2 - 2x + [(5x+a)/12]^2 = 0,
x^2 - 2x + [25x^2 + 10ax + a^2]/144 = 0,
169x^2 + (10a - 288)x + a^2 = 0 有相等的2个根,
(10a - 288)^2 - 4*169*a^2 = 0,
(10a - 288 + 2*13a)(10a - 288 - 2*13a) = 0,
(36a - 288)(-16a - 288) = 0,
a = 288/36 = 32/4 = 8或者a = -288/16 = -36/2 = -18.