If the slopes of the lines given by the equation a x^2+2 h x y+b y^2=0 are in the ratio 5: 3 , then ration h^2: a b=

Step-by-step solution

Let y=m₁ x and y=m₂ x be the lines represented by the equation. a x^2+2 h x y+b y^2=0 Then, m ₁+ m ₂= -2 ~h ~b and m ₁ ~m ₂= a b We have, m ₁ ~m ₂ = 5 3 m ₁= 5 ~m ₂ 3 aligned & 5 ~m ₂ 3 + m ₂= -2 ~h ~b and ( 5 ~m ₂ 3 ) m ₂= a b & 8 ~m ₂ 3 = -2 ~h ~b m ₂= -3 ~h 4 ~b and m ₂^2= 3 a 5 ~b & ( -3 ~h 4 ~b )^2= 3 a 5 ~b 9 ~h ^2 16 ~b ^2 = 3 a 5 ~b & h ^2 ab = 16 15 aligned