Question 1104254
You could try to use the formula, in your example number 2 in the form
{{{-4p(x-h)=(y-k)^2}}} for vertex (h,k), and p the distance from vertex to either focus or directrix.


Vertex for #2 is  (47/72, -3), and {{{p=abs(5/9-47/72)=7/72}}}.


The basic formula will then give you  {{{highlight_green(-4(7/72)(x-47/72)=(y+3)^2)}}}, which you can simplify on the left hand side.


You really should learn how to use the parabola definition to derive the equations, and also learn to use the resulting formula.