If a focal chord of the parabola $y^{2} = a x$ is $2 x - y - 8 = 0$ , then the equation of the directrix is

y + 4 = 0

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x - 4 = 0

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y - 4 = 0

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x + 4 = 0

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Solution

The correct option is D $x + 4 = 0$
Since, focal chord of parabola $y^{2} = a x$ is $2 x - y - 8 = 0$ . Also, this chord passes through focus $(\frac{a}{4}, 0)$
$∴ \frac{2 a}{4} - 0 - 8 = 0 \Rightarrow a = 16$
$∴$ Directrix is $x = - 4 \Rightarrow x + 4 = 0$

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