Question

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

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

Answer 1

The correct option is C $4$

Given, $y^2=kx-8$
$\Rightarrow y^2=k(x-\frac{8}{k})$
Shifting the origin $Y^2=kX$, where $Y=y,X=x-8/k$
Directrix of standard parabola is $X=-\frac{k}{4}$
Directrix of original parabola is $x=\frac{8}{k}-\frac{k}{4}$
Now, $x=1$ also coincides with $x=\frac{8}{k}-\frac{k}{4}$
On solving, we get $k=4$