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  4. If equation of a focal chord of the parabola y2-a x is 2 x-y-λ-0 and equation of directrix is x+4=0, then

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Q. If equation of a focal chord of the parabola $y^{2}-a x$ is $2 x-y-\lambda-0$ and equation of directrix is $x+4=0$, then

Conic Sections

Solution:

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