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If the line $x - 1 = 0$ is the directrix of the parabola $y^{2} - k x + 8 = 0$ then the value of K is

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$\frac{1}{8}$

$\frac{1}{4}$

answer is C.

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Detailed Solution

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

Directrix of this parabola is $x = - \frac{k}{4}$

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

This will coincide with $x = 1$ if

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

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