Question

If $2x + 3y + 12 = 0$ and $x - y + 4 \lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$, then $\lambda$ is equal to

• A. 2
• B. -2
• C. 3
• D. -3

Answer 1

The Correct Option is D

If $2 x +3 y +12=0$ and $x - y +4 \lambda=0$
are conjugate with respect to parabola $y ^{2}=8 x$ then $\lambda$ is equal to :
$1_{1} x +m_{1} y+ n_{1}=0$
$l _{2} x + m _{2} y + n _{2}=0$
Are conjugate with respect to parabola $y ^{2}=4 ax$
$l _{ l } n _{2}+ l _{2} n _{1}=2 am _{1} m _{2}$
$8 \lambda+12=-12$
$\lambda=-3$