Question

If a focal chord of the parabola $y^2=bx$ is $2x-y-8=0$, then the equation of the directrix is

• A. $y+4=0$
• B. $x-4=0$
• C. $y-4=0$
• D. $x+4=0$

Answer 1

The correct option is D $x+4=0$

Focal chord of parabola $y^2=bx$ always passes through its focus which is $(\frac{b}{4},0)$
Now it satisfies $2x-y-8=0$
$\therefore \frac{2b}{4}-0-8\Rightarrow b=16$
Hence, parabola will be $y^2=16x$
$\therefore a=4$
$\because$ Directrix is $x+a=0,$
$\Rightarrow x+4=0$