The length of the latus-rectum of the parabola y² + 8x − 2y + 17 = 0 is
(a) 2
(b) 4
(c) 8
(d) 16

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Solution

(c) 8

Given:
y² + 8x − 2y + 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 y²=4ax:
a = 2

Length of the latus rectum = 4a = 8 units

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