Answer:
The given equation of Parabola is
[tex]y^2 + 2 y - 2 x - 3 = 0\\\\ (y+1)^2-1-2 x- 3=0\\\\ (y+1)^2=2 x +4\\\\ (y+1)^2=2(x+2)[/tex]
The given parabola has vertex equal to (-2,-1).
If written in the form of
[tex]Y^2=4 A X[/tex]
Where , A is the focus ,if the vertex of new parabola is (0,0).
[tex]4 A=2\\\\ A=\frac{2}{4}\\\\A=\frac{1}{2}[/tex]
Coordinates of focus
[tex]=(-2,-1+\frac{1}{2})\\\\=(-2,\frac{-1}{2})[/tex]
