Question

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.

Answer 1

Y² + 2 y - 2x - 3 = 0
x + 3 = y² + 2 y
2 x + 3 = y²  + 2 x + 1 - 1
2 x + 3 = ( y + 1 )² - 1
2 x + 3 + 1 = ( y + 1 )²
Answer:
2 ( x + 2 ) = ( y + 1 )²

Answer 2

Answer:

The given equation of Parabola is

$y^2 + 2 y - 2 x - 3 = 0\\\\ (y+1)^2-1-2 x- 3=0\\\\ (y+1)^2=2 x +4\\\\ (y+1)^2=2(x+2)$

The given parabola has vertex equal to (-2,-1).

If written in the form of

$Y^2=4 A X$

Where , A is the focus ,if the vertex of new parabola is (0,0).

$4 A=2\\\\ A=\frac{2}{4}\\\\A=\frac{1}{2}$

Coordinates of focus

  $=(-2,-1+\frac{1}{2})\\\\=(-2,\frac{-1}{2})$