If the pair of straight lines 9 x 2 + a x y + 4 y 2 + 6 x + b y - 3 = 0 represents two parallel lines then

Step-by-step solution

Given, 9 x 2 + a x y + 4 y 2 + 6 x + b y - 3 = 0 represents two parallel lines, So, △ = 0 ⇒ 2 f g h + a b c - a f 2 - b g 2 - c h 2 = 0 on comparing with a x 2 + 2 h x y + b y 2 + 2 g x + 2 f y + c = 0 We get, △ = a × 3 × b 2 + 9 × 4 × - 3 - 9 b 2 2 - 4 × 9 + 3 a 2 2 = 0 ⇒ a b 2 - 3 b 2 4 + a 2 4 = 48   . . . . . . . . . . . 1 Also for parallel lines h 2 = a b ⇒ a 2 4 = 36 ⇒ a = ± 12   . . . . . . . . . 2 Now on solving equation 1   &#