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

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Solution

The correct option is C
8

Given: $y^{2} + 8 x - 2 y + 17 = 0$

$\Rightarrow (y - 1)^{2} - 1 + 8 x + 17 = 0 \Rightarrow (y - 1)^{2} + 8 x + 16 = 0$

$\Rightarrow (y - 1)^{2} = - 8 (x + 2)$

Let X=x+2,Y=y-1

$∴ Y^{2} = - 8 X$

Comparing with $y^{2} = 4 a x :$

a=2

Length of the latus rectum =4a=8 units.

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y^{2} + 8 x - 2 y + 17 = 0

Latus rectum of the parabola $y^{2} - 4 y - 2 x - 8 = 0$ is

(2, 0)

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