Answer:
(-6, 0).
Step-by-step explanation:
x^2 + 36y^2 + 12x = 0
Convert to standard form:
(x + 6)^2 - 36 +36y^2 = 0
(x + 6)^2 + 36y^2 = 36
Divide through by 36:
(x + 6)^2 / 36 + (y - 0)^2/ 36 = 1
Now compare this with the general form:
(x - h)^2/a^2 + (y - k)^2/ b^2 = 1
We see that the center (h, k) = (-6, 0).