Question

If equation of a focal chord of the parabola $y^2−ax$ is $2x−y−λ−0$ and equation of directrix is $x+4=0$, then

• A. $a+λ=48$
• B. $a+λ=12$
• C. $a+λ=36$
• D. $a+λ=24$

Answer 1

Answer: (D)

Directrix: $x=\frac{−a}{4}=−4⇒a−16$
Also, focus $\left(\frac{a}{4},0\right)⇒(4,0)$
Lies on $2x−y−λ=0$
$⇒λ=8$
$⇒λ+a−24$