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

x + 4 = 0

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x - 4 = 0

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y - 4 = 0

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y + 4 = 0

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Solution

The correct option is A
x + 4 = 0

Focal chord is any chord of a parabola which passes through the focus of the parabola. Here the given parabola is,

$y^{2} = 4 a x$

focus = (a, 0)

focal chord is given as,

2x - y - 8 = 0.This passes through (a, 0)

2a - 0 - 8 = 0

a = 4

$∴$ equation of directrix is,

x + 4 = 0

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