The length of the latus rectum of the parabola $x^{2} - 4 x - 8 y + 12 = 0$ is-

4

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6

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8

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10

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Solution

The correct option is C $8$
We have
$x^{2} - 4 x - 8 y + 12 = 0$

$\Rightarrow {(x - 2)}^{2} + 8 - 8 y = 0 (b y t a k i n g c o m m o n x)$
$\Rightarrow {(x - 2)}^{2} = 8 (y - 1)$

Comparing with $X^{2} = L . R \times Y$

So, Length of latus rectum $= 8$
Hence, the option $(C)$ is the correct answer.

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