Length of the latus rectum of the hyperbola $x y - 3 x - 4 y + 8 = 0$

4

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4 \sqrt{2}

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8

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none of these

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Solution

The correct option is B $4 \sqrt{2}$
$x y - 3 x - 4 y + 8 = 0$
$x (y - 3) - 4 (y - 3) - 12 + 8 = 0$
$(x - 4) (x y - 3) = 4$
$x y = c^{2}$ form
Latus nectum $= \frac{2 b^{2}}{a} = 2 a = 2 \sqrt{2} c$
$= 4 \sqrt{2}$
Option B $= 4 \sqrt{2}$ .

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