Question

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

y^2 + 2y - 2x - 3 = 0

Answer 1

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=(2)/(4)\\\\A=(1)/(2)`

Coordinates of focus

`=(-2,-1+(1)/(2))\\\\=(-2,(-1)/(2))`

Answer 2

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