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 $-3$

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

$l_{1}x+m_{1}y+n_1=0l_{2}x+m_{2}y+n_2=0$

Are conjugate with respect to parabola $y^2=4ax$

$l_1{n}_2+l_2{n}_1=2a{m}_1{m}_{2}8\lambda +12=-12\lambda =-3$