If one of the lines given by the equation x²+k x y+2 y²=0 is x+2 y=0 , then k =

Step-by-step solution

We have x²+k x y+2 y²=0 i.e. 1+k ( y x )+2 ( y x )²=0 Slope of line x+2 y=0 is - 1 2 Substituting y x =- 1 2 , we get 1+ k (- 1 2 )+2 (- 1 2 )²=0 1- k 2 + 1 2 =0 k =3