Question

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

Answer 1

(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

希望能解决您的问题.