Question

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

• A. $\frac{1}{8}$
• B. $8$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $4$

Given equation of parabola is
$y^2-kx+8=0$

$\Rightarrow y^2=k(x-\frac{8}{k})$

$\Rightarrow (y-0{)}^2=k(x-\frac{8}{k})$

The equation of the directrix of this parabola is

$x-\frac{8}{k}=-\frac{k}{4}$ $[\because x=-a]$

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

But the equation of the directrix is given as $x-1=0$

$\therefore \frac{8}{k}-\frac{k}{4}=1$

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

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

$\therefore k=-8,4$