1. The problem states the equation of an ellipse centered at the origin with the major axis on the y-axis is given by: $$\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1, \quad a > b$$ 2. The standard form of an ellipse centered at the origin is: $$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$$ where $(h, k)$ is the center of the ellipse. 3. Since the equation is already in standard form with no $(x-h)$ or $(y-k)$ terms, it means the center is at the origin: $$(h, k) = (0, 0)$$ 4. Therefore, the center of the ellipse is: $$(x, y) = (0, 0)$$ This means the ellipse is centered at the origin, with the major axis along the y-axis because $a > b$. Final answer: $$(x, y) = (0, 0)$$