The length of latus rectum of the parabola $y^{2} + 8 x - 2 y + 17 = 0$ is

2

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4

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8

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16

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Solution

The correct option is D $8$
The given parabola is, $y^{2} + 8 x - 2 y + 17 = 0$
$\Rightarrow (y^{2} - 2 y + 1) = - 8 x - 17 + 1 = - 8 x - 16$
$\Rightarrow (y - 1)^{2} = - 8 (x + 2)$
Comparing with standard parabola $Y^{2} = - 4 a X$
$Y = y - 1, X = x + 2, a = 2$
Hence length of latus rectum is $= 4 a = 4 \times 2 = 8$

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