The slopes of the lines given by x^2+2 h x y+2 y^2=0 are in the ratio 1: 2 , then h is

Step-by-step solution

array ll & x^2+2 h x y+2 y^2=0 & A=1, B=2, H=h array Given equation of pair of lines is Let the slopes of the lines be m ₁, ~m ₂ . m₁+m₂= -2 h 2 , m₁ m₂= 1 2 Given m₁ m₂ = 1 2 aligned & m ₁= 1 2 ~m ₂ & 1 2 ~m ₂ m ₂= 1 2 & ~m ₂^2=1 & ~m ₂= 1 aligned m ₁= 1 2 . Now, m ₁+ m ₂= -2 ~h 2 array ll & when m₁= 1 2 , m₂=1 & m₁+m₂= -2 h 2 & h= -3 2 & When m₁= -1 2 , m₂=-1 & m₁+m₂= -2 h 2 & -1 2 -1=- 2 h 2 & h= 3 2 array