Question

If the line $x-1=0$ is the directrix of the parabola $y^2-kx+8=0,k\ne 0$ and the parabola intersects the circle $x^2+y^2=4$ in two real distinc points, then the value of $k$ is

• A. $-4$
• B. $-8$
• C. $4$
• D. $Noneofthese$

Answer 1

The correct option is A $-4$

$y^2=kx-8$

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

For $e{q}^n$ of diretrix

$x-\frac{8}{k}=\frac{-k}{4}\Rightarrow x=\frac{k}{4}-\frac{8}{k}$...(1)

comparing $e{q}^n$ (1) with $x-1=0$

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

$\Rightarrow k^2-4k-3r=0$

$k=\frac{4+12}{2}\Rightarrow k=8\left(or\right)-4$