By using the center-radius form.

The center is ##C## at ##(hk)## meaning ##h = -4## and ##k = 2##.

The equation will be ##(x – h)^2 + (y – k)^2 = r^2##

That translates to:

##(x + 4)^2 + (y – 2)^2 = 25##

Expanding we get

##x^2 + 8x + 16 + y^2 – 4y + 4 = 25##

or

##x^2 + 8x + y^2 – 4y – 5 = 0##

For the graphing part locate the center ##(-42)##. Open your compass 5 units to any direction then make a circle. It should pass the following points (along with infinitely many other points):

##(-4 + 5 2)## ##->## ##(12)##

##(-4 – 52)## ##->## ##(-9 2)##

##(-4 2 + 5)## ##->## ##(-4 7)##

##(-4 2 – 5)## ##->## ##(-4 -3)##