• # question_answer The equation of the directrix of the parabola ${{\mathbf{y}}^{\mathbf{2}}}+\mathbf{4y}+\mathbf{4x}+\mathbf{2}=\mathbf{0}$is A) $2x=3$                                   B) $~x=3$         C) $3x=2$                                   D) $x=-3$

[a] Given equation of the parabola be ${{y}^{2}}+4y+4x+2=0$ ${{y}^{2}}+2.2y+4-4+4x+2=0$ ${{(y+2)}^{2}}=-4\left( x-\frac{1}{2} \right)Let\,{{y}^{2}}=-4.x$ When ${{y}^{2}}=-4a\text{ }X$ then equation of the directrix be $X=a,here\text{ }a=1\text{ }and\text{ }X=x-\frac{1}{2}~$        $\therefore x-\frac{1}{2}~=1$ $x=1+\frac{1}{2}=\frac{3}{2}\Rightarrow 2x=3$