Question

The lines 2x + 3y + 1 = 0, x + y + k = 0 are conjugate lines w.r.t. 3x²+4y² = 12. Then k =

• A. 7
• B. 17
• C. 27
• D. -7

Answer 1

Answer: (B)

17

Answer 2

Two lines l₁x + m₁y + n₁ = 0, l₂x + m₂y + n₂= 0 are conjugate lines w.r.to $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ if

a²l₁l₂ + b²m₁m₂ = n₁n₂

given l₁ = 2, m₁ = 3, n₁ = 1

l_{2 =} 1_, m₂ = 1, n₂ = k

a² = 4, b² = 3

∴ By the condition

4 x 2 x 1 + 3 x 3 x 1 = 1 x k

⇒ k = 17