If the slopes of the lines given by the equation a x²+2 h x y+b y²=0 are in the ratio 5: 3 , then the ratio h²: a b=

Step-by-step solution

(D) Let y=m₁ x and y=m₂ x be the lines represented by the equation. a x²+2 h x y+b y²=0 Then, m₁+m₂= -2 h b and m₁ m₂= a b We have, m₁ m₂ = 5 3 m₁ 5 m₂ 3 5 ~m ₂ 3 + m ₂= -2 ~h ~b and ( 5 ~m ₂ 3 ) m ₂= a b 8 m₂ 3 = -2 h b m₂= -3 h 4 b and m₂²= 3 a 5 b ( -3 h 4 b )²= 3 a 5 b 9 h² 16 b² = 3 a 5 b h ² ab = 16 15