Final answer:
With the information provided, it is not possible to determine the center of the ellipse. The coordinates for the center of an ellipse are normally represented by (h, k) in its standard equation, but the disparate information given does not lead to a conclusion.
Step-by-step explanation:
The question pertains to the determination of the center of an ellipse. However, the provided information seems insufficient or unrelated to finding the ellipse's center. In general, the standard form of an ellipse's equation is given as:
\[\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\]
where \((h, k)\) represent the coordinates of the center of the ellipse, \(a\) is the semi-major axis, and \(b\) is the semi-minor axis. To provide the direct answer, more context or a full equation of the ellipse would be necessary. None of the available choice answers can be validated with the information presented alone. Normally, the quadratic formula, given by:
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
would be used for solving quadratic equations, not directly for finding the center of an ellipse. The additional info about focus locations and a coordinate system change also doesn't directly contribute to answer this question.