Equation of the tangent at the vertex of the parabola $x^{2} + 4 x + 4 y + 16 = 0$ is

y + 3 = 0

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y + 4 = 0

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y + 2 = 0

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y + 1 = 0

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Solution

The correct option is A $y + 3 = 0$
Given $x^{2} + 4 x + 4 y + 16 = 0$
$⟹ x^{2} + 4 x + 4 + 4 (y + 3) = 0$
$⟹ (x + 2)^{2} = - 4 (y + 3)$
The equation of tangent at vertex will be $y + 3 = 0$

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