No Einstein here! Only an innocent conic

Geometry Level 4

The general equation of an ellipse is given by \(14x^2 - 4xy + 11y^2 -44x -58y + 71 =0\). If the slope of the major axis of this ellipse is \(m\) and the sum of distances of any variable point on the ellipse from its focii is \(c\), evaluate the value of \(mc^2\).

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