Question 934767
Use the distance formula and the definition of parabola.  You want the set of points equally distant from (-5,5) as from (x,-1).


{{{sqrt((x-(-5))^2+(y-5)^2)=sqrt((x-x)^2+(y-(-1))^2)}}}


{{{sqrt((x+5)^2+(y-5)^2)=sqrt((y+1)^2)}}}


{{{(x+5)^2+(y-5)^2=(y+1)^2}}}


Continue simplifying until you have an equation formula of y in terms of x.