题目

已知直线mx+ny-3=0与圆x^2+y^2+4x-1=0相切于点(-1,2),求实数m,n的值

提问时间：2021-03-27

答案

(x + 2)^2 + y^2 = 5
圆心A(-2,0),半径√5
切点(-1,2):-m + 2n - 3 = 0,m = 2n - 3
圆心与直线距离d=r = |-2m +0 - 3|/√(m^2 + n^2) = |2m + 3|/√(m^2 + n^2) = √5
m^2 - 12m + 5n^2 - 9 = 0
(2n-3)^2 -12(2n - 3) +5n^2 - 9 = 0
n^2 - 4n + 4 = 0
n = 2
m = 1