The equation of the directrix of the parabola $x^{2} - 4 x - 3 y + 10 = 0$ is

$y = - \frac{5}{4}$

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$y = \frac{5}{4}$

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$y = - \frac{3}{4}$

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$x = \frac{5}{4}$

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Solution

The correct option is B
$y = \frac{5}{4}$

The given equation can be written as $(x - 2)^{2}$ =3(y-2). Shifting the origin at (2,2) this equation reduces to $X^{2} = 3 Y, w h e r e x = X + 2, y = Y + 2.$
The directrix of this parabola with reference to new axes is Y = -a, where a= $\frac{3}{4}$
$\Rightarrow y - 2 = \frac{- 3}{4} \Rightarrow y = \frac{5}{4}$

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