No, not quite what I mean....



In the first case, where the arc angle is 90 degrees, they define the short and long axes of the ellipse of which we are using a quarter of it.

In the second case, which I crudely drew, you have center point ( 1 ), the first point of the arc ( 2 ) (the darker red dot ) and the third point ( 3 ) ( the one at the end of the grey line ).

Knowing (1), the center of the ellipse, the length from (1) to (3), and the angle of 1-2-3, it should be possible to determine the ellipse arc that passes through 1 & 3 and satisifies the angle 1-2-3.

Thus, in both cases, the center of the ellipse is in the proper position for both cases.