Directrices of the ellipse $3 x^{2} + 4 y^{2} + 12 x - 8 y - 32 = 0$ are:

x = 6, x = - 10

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x = 5, x = - 11

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x = 4, x = 12

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x = 3, x = 9

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Solution

The correct option is A $x = 6, x = - 10$
$3 x^{2} + 4 y^{2} + 12 x - 8 y - 32 = 0$
$\Rightarrow \frac{{(x + 2)}^{2}}{16} + \frac{{(y - 1)}^{2}}{12} = 1$
$e = \sqrt{1 - \frac{12}{16}} = \frac{1}{2}$
The equation of directrix is $x = h \pm \frac{a}{e}$
$\Rightarrow x = - 2 \pm 8$
$\Rightarrow x = 6, x = - 10$

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