Question 1039377
You can use those pieces of information and the distance formula to derive the equation.   A set of points (x,y)  is the same distance from  (-4,9) as from (x,-3).  Put into the formula,


{{{sqrt((x-(-4))^2+(y-9)^2)=sqrt((x-x)^2+(y-(-3))^2)}}}.
Simplify this.

First step after that initial equation could be
{{{(x+4)^2+(y-9)^2=(y+3)^2}}}
and keep going to whatever form of the equation you need for making a comparison to your choices.



Study this demonstration:
<a href="https://www.youtube.com/watch?v=Wworlx39KfQ">Equation of parabola given focus and directrix - Vertex not at the origin - video</a>