If $x - 1 = 0$ is the directix of parabola $y^{2} - k x + 8 = 0$ , then $k$ is equal to

1 / 8

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8

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4

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1 / 4

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Solution

The correct option is A $4$
We have, $y^{2} - k x - 8 = 0$
$\Rightarrow y^{2} = k (x - \frac{8}{k})$
$∴$ Directrix $x - \frac{8}{k} = - \frac{k}{4}$
$\Rightarrow x - (\frac{8}{k} - \frac{k}{4}) = 0$
But equation of directrix is $x - 1 = 0$ . Hence, by comparing, we get
$\frac{8}{k} - \frac{k}{4} = 1 \Rightarrow k^{2} + 4 k - 32 = 0$
$\Rightarrow (k - 4) (k + 8) = 0$
$\Rightarrow k = 4, - 8$ .

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