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. $1/8$
• B. $8$
• C. $4$
• D. $1/4$

Answer 1

The correct option is C $4$

The parabola is $y^2-kx+8=0$

$\Rightarrow$ $y^2=kx-8$

$=k(x-\frac{8}{k})$

$=4AX$

Where $4A=k$

Direction of the parabola is $X+A=0$

Comparing it with $x-1=0$ we get,

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

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

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

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

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

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

$\therefore$ $k=-8,4$

$\therefore$ From the given options one of the value of $k$ is $4$