The line $x - 1 = 0$ is the directrix of the parabola $y^{2} - k x + 8 = 0.$ Then one of the values of $k$ is

\frac{1}{8}

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8

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4

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\frac{1}{4}

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Solution

The correct option is C $4$
$y^{2} - k x + 8 = 0$
$y^{2} = k (x - 8 / k) \Rightarrow Y^{2} = 4 a X$ where $Y = y, 4 a = k, X = (x - 8 / k)$
so directrix of this parabola is $X = - a = - \frac{k}{4} \Rightarrow x = \frac{8}{k} - \frac{k}{4}$
and given $\frac{8}{k} - \frac{k}{4} = 1 \Rightarrow k^{2} + 4 k - 32 = 0 \Rightarrow k = 4, - 8$

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