The value of k , if the slope of one of the lines given by 4 x^2+ k x y+y^2=0 is four times that of the other, is given by

Step-by-step solution

Given equation of pair of lines is aligned & 4 x^2+ k x y+y^2=0 & a =4, ~h = k 2 , ~b =1 aligned According to the given condition, aligned & m ₁=4 ~m ₂ & ~m ₁+ m ₂=- k & 4 ~m ₂+ m ₂=- k & 5 ~m ₂=- k & ~m ₂= k 5 ...(i) & ~m ₁ ~m ₂=4 & (4 ~m ₂ ) m ₂=4 & ~m ₂^2=1 & ~m ₂= 1 aligned From (i), k = 5