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 distinct points, then the value of $k$ is?

• A. $-4$
• B. $-8$
• C. $4$
• D. $8$

Answer 1

Answer: (B)

$-8$

$y^2=(kx-8)$

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

$\Rightarrow a=\frac{k}{4}$

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

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

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

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

Parabola and circle intersects exactly at two different points only if $k=-8.$