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where and are, as usual, the lengths of the axes. This is simply because when and when , so the centre has shifted from to .
In the example you've given, the centre is at the mid-point of the line joining to ; i.e. at . So .
The length of the vertical axis is (the distance between these vertices), so .
The foci always lie on the major axis, so since one focus is at , the major axis is vertical, and the foci are at a distance from the centre. So . And, when the major axis is vertical, .
Putting all this together, I reckon the equation is:
I hope that answers some of your questions.