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Slope Form a Line

The equation ...

Question

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

x = - 2

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x = 2

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y = 2

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y = - 2

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Solution

The correct option is C $y = 2$
Given that
$x^{2} + 4 x + 2 y = 0$
$x^{2} + 4 x + 2 y + 4 - 4 = 0$
$(x + 2)^{2} = - 2 (y - 2)$
Which is of the form
$X^{2} = - 2 Y$
So,the equation of tangent at vertex is $Y = 0$
i.e., $y - 2 = 0$
$\Rightarrow y = 2$

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