If $y^{2} + 2 y - x + 5 = 0$ represents a parabola, then the length (in units) of the latus rectum is

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Solution

Given : $y^{2} + 2 y - x + 5 = 0$
$\Rightarrow y^{2} + 2 y + 1 = x - 4$
$\Rightarrow (y + 1)^{2} = (x - 4)$
Comparing with standard equation of parabola $Y^{2} = 4 a X,$
$4 a = 1$
$∴$ Length of latus rectum $= 4 a = 1$ unit

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