Question 913811
This is not a solution, but just advice:


Study how the equation of a parabola is derived using the distance formula, the meaning and use of focus and directrix, and the definition of a parabola.   Simplify the distance formula equation and check how the resulting formula appears.  That would be how to derive the equation of a parabola.


What you want to do is work in the other direction, so you would use the parts the resulting derived parabola equation to find the focus and directrix.


Like I say, this is advice or guidance, but not the answer you requested.
Your textbook should show a very good derivation for the equation of a parabola.  Say if otherwise.


Note that in your second equation, the vertex would have moved from the standard reference (0,0) to  the new vertex point (-3,5).