Find length of latus rectum of the parabola $y^{2} - 2 y = - 2 x - 3$ .

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Solution

The correct option is A $2$
$y^{2} - 2 y = - 2 x - 3$
Adding 1 on both sides, we get
$⟹ y^{2} - 2 y + 1 = - 2 x - 2$
$⟹ (y - 1)^{2} = - 2 (x - 1)$

Comaring with the standard equation, $(y - k)^{2} = - 4 a (x - h)$ ,we get $4 a = 2$
Length of latus rectum $= 4 a = 2$

So, the answer is option (A).

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