Question 1008214
Standard Form Equation for a Circle, {{{(x-h)^2+(y-k)^2=r^2}}}, center (h,k) and radius r.


Your given circle has center   (?,-4), you do not immediately know the x coordinate.  You only know that (0,0) is a point on the circle, r=5, and some unknown point (x,-4) is therefore 5 units distance from the origin (0,0).  In an equation, 


{{{sqrt((x-0)^2+(-4-0)^2)=5}}}


{{{sqrt(x^2+16)=5}}}


{{{x^2+16=25}}}


{{{x^2=9}}}


{{{x=0+- 3}}}
Center can be  (-3,-4) or  (3,-4).


Circle can be  {{{system((x+3)^2+(y+4)^2+25,  or,  (x-3)^2+(y+4)^2=25)}}}.