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

8

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6

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4

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2

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Solution

The correct option is B $4$
$y^{2} - 4 x + 4 y + 8 = 0$
$\Rightarrow y^{2} + 4 y + 4 = 4 x - 4$ , rewrite above equation
$\Rightarrow (y + 2)^{2} = 4 (x - 1)$
Comparing with standard equation $Y^{2} = 4 a X$
$Y = y + 2, X = x - 1, a = 1$

Therefore length of latus rectum $= 4 a = 4 \cdot 1 = 4$

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