the equation of a circle is defined by: [tex] (x - h)^{2} + (y - k)^{2} = r^{2} [/tex] where (h,k) is the center of the circle and "r" is the radius. So we need to find the radius, which is the distance between the center (-1,-4) and the point on the circle (-4, 0). Do this using the distance formula: d = [tex] \sqrt{( x_{2 -} x_{1})^2 + ( y_{2}- y_{1})^2 } [/tex]
so distance = [tex] \sqrt{(-4 - 0)^2 + (-1 + 4)^2} = \sqrt{25} = 5[/tex]
Now we just write the equation: [tex] (x +1)^2 + (y + 4)^2 = 25[/tex]