The equation $y^{2} + 4 x + 4 y + k = 0$ represents a parabola whose latus rectum is

1

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2

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3

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4

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Solution

The correct option is B $4$
$y^{2} + 4 x + 4 y + k = 0$
$y^{2} + 2 \times 2 y + 4 - 4 + 4 x + k = 0$
$(y + 2)^{2} = - 4 x - k + 4$
$(y + 2)^{2} = - 4 (x - \frac{4 + k}{4})$
$∴$ Latus rectum $= 4$ units

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4

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