If 4 a b=3 h^2 , then the ratio of the slope of lines represented by a x^2+2 h x y+b y^2=0 is

Step-by-step solution

aligned & Here, m₁+m₂= -2 h b ...(i) & and m ₁ ~m ₂= a ~b . & (m₁-m₂ )^2= (m₁+m₂ )^2-4 m₁ m₂ & = 4 h^2-4 a b b^2 & = 4 h^2-3 h^2 b^2 [ 4 a b=3 h^2 (given) ] & = h^2 b^2 aligned m ₁- m ₂= h ~b ...(ii) On solving (i) and (ii), we get aligned & m₁= -h 2 b and m₂= -3 h 2 b & m₁: m₂=1: 3 aligned