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

Step-by-step solution

Given, equation of lines x^2+2 h x y+2 y^2=0...(i) On comparing with a x^2+2 h x y+b y^2=0 a=1 and b=2 Let y=m₁ x and y=m₂ x be the lines, whose combined form is Eq. (i) m₁+m₂= -2 h b = -2 h 2 =-h...(ii) and m₁ m₂=a / b=1 / 2...(iii) aligned & m₁: m₂=1: 2 & m₁ m₂ = 1 2 m₂=2 m₁ aligned From Eq. (ii), we get m₁+m₂=-h and from Eq. (iii) we get array llrl m₁+2 m₁=-h & and & m₁ m₂ & = 1 2 m₁=-h / 3 & and & 2 m₁^2 & = 1 2 - h 3 = 1 2 h= 3 2 & and & m₁ & = 1 2 array