If x^2 a + 2 x y ~h + y^2 ~b =0 represents a pair of straight lines and slope of one of the lines is twice that of the other, then a b: h^2 is [Note: The question has been modified to get the correct answer.]

Step-by-step solution

m ₁: m ₂=1: 2 If the slopes of the lines given by a x^2+2 ~h x y+ b y^2=0 are in the ratio m:n, then ⁻( m + n )^2 ab =4 mnh ^2 (1+2)^2 ( 1 a ) ( 1 b )=4(1)(2) ( 1 h )^2 a b h^2 = 9 8 [Note: In the question, x^2 a ^2 is changed to x^2 a to apply appropriate textual concepts.]