For the parabola y 2 + 6 y - 2 x + 5 = 0 , match the items in List- I with the suitable item in List- II…

Given:

$y^2+6y-2x+5=0$

$\Rightarrow {\left(y+3\right)}^2=2x+4$

$\Rightarrow {\left(y+3\right)}^2=2\left(x+2\right)$

The form: ${\left(y-k\right)}^2=4a\left(x-h\right)$, where, the vertex is $V\left(h,k\right)$

Therefore,

Vertex $\equiv \left(-2,-3\right)$

Now, $4a=2\Rightarrow a=\frac{1}{2}$

Now, we know that focus lies at a distance $a$ from the vertex of the parabola.

Therefore,

$-2+a=-2+\frac{1}{2}=\frac{-3}{2}$

So, coordinates of focus are $\left(\frac{-3}{2},-3\right)$

Equation of directrix in standard form is $x+a=0$ from the vertex.

Therefore, equation of directrix is 

$x=-2-\frac{1}{2}=-\frac{5}{2}$

or $2x+5=0$

And, axes is $y=-3 \text{or} y+3=0$.