Question

If the pair of straight lines $9x^2 + axy + 4y^2 + 6x + by - 3 = 0$ represents two parallel lines then

• A. $a = 6, b = 2$
• B. $a = 12, b = 4$
• C. $a = 3, b = 1$
• D. $a = -12, b = 4$

Hint:

Use the discriminant condition $a^2 = 4bc$ for general second-degree equations to check parallel lines.

Answer 1

The Correct Option is B

For a pair of straight lines to be parallel:
The discriminant must be zero $\Rightarrow a^2 - 4(9)(4) = 0 \Rightarrow a^2 = 144 \Rightarrow a = \pm 12$
Choose $a = 12$ from the options. Now verify values with conditions for consistency — plug into original equation and check conditions for parallelism