Question

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.
• B. 8
• C. 4
• D.

Answer 1

The correct option is C

4

The parabola is $y^2=4.\frac{k}{4}(x-\frac{8}{k})$.
Putting y=Y, x-$\frac{8}{k}$=X, the equation is $Y^2=4.\frac{k}{4}.X$
$\therefore$ The directrix is $X+\frac{k}{4}=0,i.e.x-\frac{8}{k}+\frac{k}{4}=0$.
But x-1=0 is the directrix. So, $\frac{8}{k}-\frac{k}{4}=1\Rightarrow k=-8,4$.