Coordinates

Whenever you see a circle in the form $Ax^2 + Ay^2 + Bx + Cy + D = 0$, complete the squares to get something like $(x - h)^2 + (y - k)^2 = r^2$, then the center will just be (h, k) and the radius will just be r.

So, for this one, you move every term to the left-hand side first.

$x^2 + y^2 + 4x + 16y - 18 = 0$

Now, complete the square.

$(x^2 + 4x + 4) - 4 + (y^2 + 16y + 64) - 64 - 18 = 0\\ (x + 2)^2 - 4 + (y + 8)^2 - 64 - 18 = 0\\ (x + 2)^2 + (y + 8)^2 = 86$

Can you take it from here to identify h and k?

Hint: You can write $x + a$ as $x - (-a)$ at all times.