Rewrite the equation y^2 - 2x + 2y-5=0 in standard form. determine the focus and directrix

Answer : option D

We apply completing the square method

Move all the y terms on one side

y^2 +2y = 2x + 5

In completing the square method , we take coefficient of y then divide it by 2  and square it

2/2 =1  then 1^2 = 1

Add it on both sides

Solve for x

(divide by 2 on both sides)

Vertex is (h,k) that is (-3,-1). h= -3  and k = -1

The value of a= 1/2

Plug in 1/2 for 'a'

so P = 1/2

Focus = (h+p, k)

h= -3  and k = -1, p = 1/2

Directrix x=(h - P)

Option D is correct

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