Given:
[tex]x^2+4x+2y+2=0[/tex][tex]\begin{gathered} x^2+4x+4-4+2y+2=0 \\ x^2+4x+4+2y-2=0 \\ x^2+4x+4=2-2y \\ (x+2)^2=-2(y-1) \\ X^2=-2Y \end{gathered}[/tex]
Compare with,
[tex]x^2=-4ay[/tex][tex]\begin{gathered} 4a=2 \\ a=\frac{1}{2} \end{gathered}[/tex][tex]\text{Directrix : y=}\frac{3}{2}[/tex][tex]\text{Focus: (-2,}\frac{1}{2})[/tex][tex]\text{Vertex: (-2,1)}[/tex]
