The equation of the directrix of the parabola y 2 + 4 y + 4 x + 2 = 0 is [2001]

Question

The equation of the directrix of the parabola $y^{2} + 4 y + 4 x + 2 = 0$ is [2001]

Smart Achievers · Accepted Answer

(4)

Given equation of the parabola is $y^{2} + 4 y + 4 x + 2 = 0$

$\Rightarrow y^{2} + 4 y + 4 = - 4 x + 2$ $\Rightarrow {(y + 2)}^{2} = - 4 (x - \frac{1}{2})$

It is of the form $Y^{2} = - 4 A X$

Equation of whose directrix is given by $X = A$

$∴$ Equation of required directrix is $x - \frac{1}{2} = 1$ $\Rightarrow x = \frac{3}{2}$

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