1. In the form (x - h)^2 + (y - k)^2 = r^2, the center is (h, k)
So we have
(x + 7)^2 + (y - 13)^2 = 196
(x - (-7) )^2 + (y - 13)^2 = 196
So.....the center is (-7, 13)
2. x^2 + y^2 + 14x + 10y - 7 = 0 re-write as
x^2 + 14x + y^2 + 10y = 7 complete the square on x and y
x^2 + 14x + 49 + y^2 + 10y + 25 = 7 + 49 + 25 factor and simplify
(x + 7)^2 + (y + 5)^2 = 81
So....the center is (-7, -5)
3. Hyperbola