Question

If $x-1=0$ is the directrix of parabola $y^2-kx+8=0$, then one of the value of $k$ is

• A. $-8$
• B. $-\frac{4}{3}$
• C. $8$
• D. $-4$

Answer 1

The correct option is A $-8$

$y^2=k(x-\frac{8}{k})$ or $y^2=4\left(\frac{k}{4}\right)(x-\frac{8}{k})$

Compare with $y^2=4aX$

$(a=\frac{k}{4},X=x-\frac{8}{k})$

$\therefore$ Equation of directrix
$X+a=0$

$\Rightarrow x-\frac{8}{k}+\frac{k}{4}=0\Rightarrow x=-\frac{k}{4}+\frac{8}{k}$

$\Rightarrow 4k=32-k^2$ (using $x=1$ as the directrix)

$\Rightarrow k^2+4k-32=0\Rightarrow (k+8)(k-4)=0$

$k=4,-8$

Hence (a) is correct answer.